Inspired by CapsNet's routing-by-agreement mechanism with its ability to learn object properties, we propose a CapsNet architecture with object coordinate atoms and a modified routing-by-agreement algorithm with unevenly distributed initial routing probabilities. The model is based on CapsNet but uses a routing algorithm to find the objects' approximate positions in the image coordinate system. We also discussed how to derive the property of translation through coordinate atoms and we discover the importance of sparse representation. We train our model on the single moving MNIST dataset with class labels. Our model can learn and derive the coordinates of the digits better than its convolution counterpart that lacks a routing-by-agreement algorithm, and can also perform well when testing on the multi-digit moving MNIST datasets. When deriving the coordinates, our model performs at least 13 , 24 , and 51 better than the convNet counterpart and ResNet 20 benchmarks on 1-digit, 2-digit, and 3-digit moving MNIST datasets. This shows our method has better transfer learning properties on unseen scenarios of the new but related datasets. We also achieve slightly better performance than the ResNet benchmark in the KTH dataset; these results show our method reaches the state-of-art performance on object localization without any extra localization techniques and modules as in prior work.
A capsule is a group of neurons whose outputs represent different properties of the same entity. Each layer in a capsule network contains many capsules [a group of capsules forms a capsule layer and can be used in place of a traditional layer in a neural net]. We describe a version of capsules in which each capsule has a logistic unit to represent the presence of an entity and a 4x4 matrix which could learn to represent the relationship between that entity and the viewer (the pose). A capsule in one layer votes for the pose matrix of many different capsules in the layer above by multiplying its own pose matrix by trainable viewpoint-invariant transformation matrices that could learn to represent part-whole relationships. Each of these votes is weighted by an assignment coefficient. These coefficients are iteratively updated for each image using the Expectation-Maximization algorithm such that the output of each capsule is routed to a capsule in the layer above that receives a cluster of similar votes. The transformation matrices are trained discriminatively by backpropagating through the unrolled iterations of EM between each pair of adjacent capsule layers. On the smallNORB benchmark, capsules reduce the number of test errors by 45 compared to the state-of-the-art. Capsules also show far more resistance to white box adversarial attack than our baseline convolutional neural network. A capsule is a group of neurons whose activity vector represents the instantiation parameters of a specific type of entity such as an object or object part. We use the length of the activity vector to represent the probability that the entity exists and its orientation to represent the instantiation parameters. Active capsules at one level make predictions, via transformation matrices, for the instantiation parameters of higher-level capsules. When multiple predictions agree, a higher level capsule becomes active. We show that a discrimininatively trained, multi-layer capsule system achieves state-of-the-art performance on MNIST and is considerably better than a convolutional net at recognizing highly overlapping digits. To achieve these results we use an iterative routing-by-agreement mechanism: A lower-level capsule prefers to send its output to higher level capsules whose activity vectors have a big scalar product with the prediction coming from the lower-level capsule.