In this paper, we formalize the idea behind capsule nets of using a capsule vector rather than a neuron activation to predict the label of samples. To this end, we propose to learn a group of capsule subspaces onto which an input feature vector is projected. Then the lengths of resultant capsules are used to score the probability of belonging to different classes. We train such a Capsule Projection Network (CapProNet) by learning an orthogonal projection matrix for each capsule subspace, and show that each capsule subspace is updated until it contains input feature vectors corresponding to the associated class. With low dimensionality of capsule subspace as well as an iterative method to estimate the matrix inverse, only a small negligible computing overhead is incurred to train the network. Experiment results on image datasets show the presented network can greatly improve the performance of state-of-the-art Resnet backbones by $10-20\%$ with almost the same computing cost.

Then, one can adopt theprinciple of separatingthe presence of an entity and its instantiation parameters into capsule length and orientation, respectively. In particular, we use the lengths of capsules to score the presence of entity classes corresponding to different subspaces, while their orientations are used to instantiate the parameters of entity properties such as poses, scales, deformations and textures.

In this paper, we formalize the idea behind capsule nets of using a capsule vector rather than a neuron activation to predict the label of samples. To this end, we propose to learn a group of capsule subspaces onto which an input feature vector is projected. Then the lengths of resultant capsules are used to score the probability of belonging to different classes. We train such a Capsule Projection Network (CapProNet) by learning an orthogonal projection matrix for each capsule subspace, and show that each capsule subspace is updated until it contains input feature vectors corresponding to the associated class. With low dimensionality of capsule subspace as well as an iterative method to estimate the matrix inverse, only a small negligible computing overhead is incurred to train the network. Experiment results on image datasets show the presented network can greatly improve the performance of state-of-the-art Resnet backbones by $10-20\%$ with almost the same computing cost.

In this paper, we do not intend to introduce some brand new architectures for capsule nets.

This paper introduces an alternative to CNN based architectures being inspired by the recently proposed capsule networks. The authors proposed to replace the last layer of ResNet variants by a capsule projection network, thereby getting promising results on the CIFAR and SVHN datasets. However, the motivation for using a capsule projection layer is unclear even though the technique is straightforward and easy to implement with minor computational overhead. The main idea of the capsule projection layer is to project the input feature vector to some learnt capsule subspaces (one for each class in classification setting), which are then used to distinguish between the different classes in classification. The authors also show that this projection technique leads to computation of gradients which are orthogonal to the learnt subspace, enabling discovery of novel characteristics leading to improvement of the learnt subspace.

In this paper, we formalize the idea behind capsule nets of using a capsule vector rather than a neuron activation to predict the label of samples. To this end, we propose to learn a group of capsule subspaces onto which an input feature vector is projected. Then the lengths of resultant capsules are used to score the probability of belonging to different classes. We train such a Capsule Projection Network (CapProNet) by learning an orthogonal projection matrix for each capsule subspace, and show that each capsule subspace is updated until it contains input feature vectors corresponding to the associated class. With low dimensionality of capsule subspace as well as an iterative method to estimate the matrix inverse, only a small negligible computing overhead is incurred to train the network.

In this paper, we formalize the idea behind capsule nets of using a capsule vector rather than a neuron activation to predict the label of samples. To this end, we propose to learn a group of capsule subspaces onto which an input feature vector is projected. Then the lengths of resultant capsules are used to score the probability of belonging to different classes. We train such a Capsule Projection Network (CapProNet) by learning an orthogonal projection matrix for each capsule subspace, and show that each capsule subspace is updated until it contains input feature vectors corresponding to the associated class. We will also show that the capsule projection can be viewed as normalizing the multiple columns of the weight matrix simultaneously to form an orthogonal basis, which makes it more effective in incorporating novel components of input features to update capsule representations. In other words, the capsule projection can be viewed as a multi-dimensional weight normalization in capsule subspaces, where the conventional weight normalization is simply a special case of the capsule projection onto 1D lines. Only a small negligible computing overhead is incurred to train the network in low-dimensional capsule subspaces or through an alternative hyper-power iteration to estimate the normalization matrix. Experiment results on image datasets show the presented model can greatly improve the performance of the state-of-the-art ResNet backbones by 10 20% and that of the Densenet by 5 7% respectively at the same level of computing and memory expenses. The CapProNet establishes the competitive state-of-the-art performance for the family of capsule nets by significantly reducing test errors on the benchmark datasets.

In this paper, we formalize the idea behind capsule nets of using a capsule vector rather than a neuron activation to predict the label of samples. To this end, we propose to learn a group of capsule subspaces onto which an input feature vector is projected. Then the lengths of resultant capsules are used to score the probability of belonging to different classes. We train such a Capsule Projection Network (CapProNet) by learning an orthogonal projection matrix for each capsule subspace, andshow that each capsule subspace is updated until it contains input feature vectors corresponding to the associated class. We will also show that the capsule projection can be viewed as normalizing the multiple columns of the weight matrix simultaneously to form an orthogonal basis, which makes it more effective in incorporating novel components of input features to update capsule representations. In other words, the capsule projection can be viewed as a multidimensional weight normalization in capsule subspaces, where the conventional weight normalization is simply a special case of the capsule projection onto 1D lines. Only a small negligible computing overhead is incurred to train the network in low-dimensional capsule subspaces or through an alternative hyper-power iteration to estimate the normalization matrix. Experiment results on image datasets show the presented model can greatly improve the performance of the state-of-the-art ResNet backbones by10 20% and that of the Densenet by 5 7% respectively at the same level of computing and memory expenses. The CapProNet establishes the competitive state-of-the-artperformance for the family of capsule nets by significantly reducing test errors on the benchmark datasets.