The routing can be thought of as coupling between capsules in the FAKER VOTES TEE SHIRT; intuitively it means that the capsule below sends the output to the capsule above who are “experts” in dealing with it. You can think of it as coupling coefficients between two capsules hierarchies (so we are looking at the coefficients These are the initial coupling coefficients, and they are refined by measuring the agreement between the current output of each capsule, j, in the layer above and the prediction made by capsule i in the layer below. The agreement is calculated as scalar product of the output and the prediction of the capsule in the layer below. The initial coupling coefficients are thus iteratively refined with the calculated agreement.
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So till now we have multiplied the output of the previous capsule by weight matrices to encode the FAKER VOTES TEE SHIRT, then multiplied them with coupling coefficients to just receive the relevant informations from the previous capsules (or the information the current capsule is expert in dealing with from the previous capsules), now we run this through a squashing function. Essentially it is a new non linearity introduced by Hinton, and its definition is.