We follow the idea of formulating vision as inverse graphics and propose a new type of element for this task, a neural-symbolic capsule. It is capable of de-rendering a scene into semantic information feed-forward, as well as rendering it feed-backward. An initial set of capsules for graphical primitives is obtained from a generative grammar and connected into a full capsule network. Lifelong meta-learning continuously improves this network's detection capabilities by adding capsules for new and more complex objects it detects in a scene using few-shot learning. Preliminary results demonstrate the potential of our novel approach.
In @cite_29 Hinton al introduced capsules, extending the idea of classical neurons by allowing them to output vectors instead of scalars. These vectors can be interpreted as attributes of an object and aim to reduce information-loss between layers of convolutional neural networks (CNN) @cite_18 @cite_22 . Capsules require specialized routing protocols, such as routing-by-agreement @cite_25 , where the activation probability of a capsule is dependent on the agreement of its real inputs with their expected values. Further extensions for capsules have been proposed, such as using matrices internally @cite_21 or using 3D input @cite_5 .
@cite_18 @cite_22 @cite_29 @cite_21 @cite_5 @cite_25
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We present group equivariant capsule networks, a framework to introduce guaranteed equivariance and invariance properties to the capsule network idea. Our work can be divided into two contributions. First, we present a generic routing by agreement algorithm defined on elements of a group and prove that equivariance of output pose vectors, as well as invariance of output activations, hold under certain conditions. Second, we connect the resulting equivariant capsule networks with work from the field of group convolutional networks. Through this connection, we provide intuitions of how both methods relate and are able to combine the strengths of both approaches in one deep neural network architecture. The resulting framework allows sparse evaluation of the group convolution operator, provides control over specific equivariance and invariance properties, and can use routing by agreement instead of pooling operations. In addition, it is able to provide interpretable and equivariant representation vectors as output capsules, which disentangle evidence of object existence from its pose. Convolutional neural networks (CNNs) have shown remarkable results over the last several years for a wide range of computer vision tasks. A new architecture recently introduced by , referred to as a capsule networks with dynamic routing, has shown great initial results for digit recognition and small image classification. The success of capsule networks lies in their ability to preserve more information about the input by replacing max-pooling layers with convolutional strides and dynamic routing, allowing for preservation of part-whole relationships in the data. This preservation of the input is demonstrated by reconstructing the input from the output capsule vectors. Our work expands the use of capsule networks to the task of object segmentation for the first time in the literature. We extend the idea of convolutional capsules with locally-connected routing and propose the concept of deconvolutional capsules. Further, we extend the masked reconstruction to reconstruct the positive input class. The proposed convolutional-deconvolutional capsule network, called SegCaps, shows strong results for the task of object segmentation with substantial decrease in parameter space. As an example application, we applied the proposed SegCaps to segment pathological lungs from low dose CT scans and compared its accuracy and efficiency with other U-Net-based architectures. SegCaps is able to handle large image sizes (512 x 512) as opposed to baseline capsules (typically less than 32 x 32). The proposed SegCaps reduced the number of parameters of U-Net architecture by 95.4 while still providing a better segmentation accuracy. 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.