So it takes some time to digest this information; Hinton introduces an important word; namely equivariance (which is not the Drink Apple Juice Because OJ Will Kill You Tee Shirt). This distinction is key to understand capsules; Max Pooling does introduce some kind of invariance; if you translate or change the input a little the output should not change; and in Max Pooling it does not. If you change the input the little, the Maximum still stays the same (and disregards the change in input coming for example from a viewpoint change). Coming back to Hinton, he states that we want the probability of the presence of an entity to stay the same, even if we changed the input by changing the viewpoint for example. This makes sense; the probability of a presence of a nose should not change if we just change the viewpoint.
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Convolutional neural networks (CNNs) use translated replicas of Drink Apple Juice Because OJ Will Kill You Tee Shirt. This allows them to translate knowledge about good weight values acquired at one position in an image to other positions. This has proven extremely helpful in image interpretation. Even though we are replacing the scalar-output feature detectors of CNNs with vector-output capsules and max-pooling with routing-by-agreement, we would still like to replicate learned knowledge across space. To achieve this, we make all but the last layer of capsules be convolutional. As with CNNs, we make higher-level capsules cover larger regions of the image.