Next, we multiply the prediction vectors by the coupling coefficients . The coupling coefficients exist between any two capsules. We know that capsules from the lower layer send their output to the capsules in the higher layer. The coupling coefficient helps the capsule in the lower layer to understand which capsule in the higher layer it has to send its output to.

For instance, let's consider the same example, where we are trying to predict whether an image consists of a face. represents the agreement between and .

represents the agreement between an eye and a face. Since we know that the eye is on the face, the value will be increased. We know that the prediction vector implies the predicted position of the face based on the eyes. Multiplying by implies that we are increasing the importance of the eyes, as the value of is high.

represents the agreement between nose and face. Since we know that the nose is on the face, the value will be increased. We know that the prediction vector implies the predicted position of the face based on the nose. Multiplying by implies that we are increasing the importance of the nose, as the value of is high.

Let's consider another low-level feature, say, , which detects a finger. Now, represents the agreement between a finger and a face, which will be low. Multiplying by implies that we are decreasing the importance of the finger, as the value of is low.

But how are these coupling coefficients learned? Unlike weights, the coupling coefficients are learned in the forward propagation itself, and they are learned using an algorithm called dynamic routing, which we will discuss later in an upcoming section.

After multiplying by , we sum them up, as follows:

Thus, we can write our equation as follows: