Routing by Agreement is a mechanism in capsule networks that controls the flow of information between capsule layers by evaluating the agreement between the predictions of the lower capsules and the outputs of the upper capsules.
Capsules are groups of neurons that represent features as vectors.
In routing by agreement, it is iteratively calculated how well the prediction of a lower capsule matches the output of an upper capsule.
The connection strength (routing coefficient) is adjusted based on this agreement, so that capsules with similar predictions are more strongly connected.
This mechanism allows the network to model hierarchical relationships between parts of objects and the whole, and improves recognition under variations in the input.