Abstract
Capsule network (CapsNet) can recognize the objects by encoding the part–whole relationships in a way similar to our human perceptual system and has already shown its great potential in image classification tasks. However, it is limited to the real domain while the complex numbers having much richer representational capacity and facilitating the noise-robust memory retrieval mechanisms. Therefore, we propose two architectures: Complex-valued Dense CapsNet (Cv-CapsNet) and Complex-valued Diverse CapsNet (Cv-CapsNet++), each of them consists of three stages. In the first stage, multi-scale complex-valued features are obtained by the restricted dense complex-valued subnetwork. Particularly, Cv-CapsNet++ utilizes a three-level Cv-CapsNet hierarchical model to extract the multi-scale high-level complex-valued features in order to adapt to the complicated datasets. In the second stage, these complex-valued features are encoded into the complex-valued primary capsules, Particularly, Cv-CapsNet++ encodes the complex-valued features from different hierarchies into the multi-dimensional complex-valued primary capsules. In the third stage, we generalize the dynamic routing algorithm to the complex-valued domain and employ it to fuse the real- and imaginary-valued information of complex-valued primary capsules. The experimental results show that the proposed architectures lead to fewer trainable parameters, better performance, and fewer iterations during training than Real-valued CapsNets (Rv-CapsNets) with similar structure and original CapsNet on FashionMNIST and CIFAR10 datasets.
Highlights
Convolution Neural Networks (CNNs) [1] have extensive learning capacity and can infer the attributes of input images without prior knowledge, which makes them the state-of-theart architectures in many image classification tasks
CNNs have several drawbacks specially related to the sub-sampling layers
Sub-sampling layers often give a small amount of translation invariance but lose the location and pose information, which leads to the fact that their parameters obtained from data training are more inclined to memorize and reproduce features rather than understand them, in particular, ignoring spatial relationships between them which can be valuable for image classification
Summary
Convolution Neural Networks (CNNs) [1] have extensive learning capacity and can infer the attributes of input images without prior knowledge, which makes them the state-of-theart architectures in many image classification tasks. More robust to attacks of samples with misled location and pose information than CNNs. the original CapsNet has its shortcomings, as it uses a shallow network to extract features, which makes it unsuitable for complicated datasets and its large convolutional kernels increases its trainable parameters. Cv-CapsNet++ utilizes a 3-level Cv-CapsNet hierarchical model to extract multi-scale high-level complex-valued features to adapt to complicated datasets such as CIFAR10. These complexvalued features are encoded into the complex-valued primary capsule, while in Cv-CapsNet++ complex-valued features extracted at different hierarchies are encoded into complex-valued primary capsules of different dimensions. This paper has following contributions: (i) We propose restricted complex-valued dense network and complex-valued capsule encoding unit. (ii) We generalize the dynamic routing algorithm to complex-valued domain and employ it to fuse the real-valued and imaginary-valued information of complex-valued primary capsules, which greatly decreases the number of trainable parameters of complexvalued routing models than real-valued routing models with same dimension capsules. (iii) We propose Cv-CapsNet and Cv-CapsNet++, which leads to fewer trainable parameters, better performance, and fewer iterations during training than Rv-CapsNets with similar structure and original CapsNet on FashionMNIST and CIFAR10 datasets
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