In this work, we propose a novel and surprisingly simple routing strategy called self-routing, where each capsule is routed independently by its subordinate routing network. Therefore, the agreement between capsules is not required anymore, but both poses and activations of upper-level capsules are obtained in a way similar to Mixture-of-Experts. Our experiments on CIFAR10, SVHN, and SmallNORB showthat the self-routing performs more robustly against white-box adversarial attacks and affine transformations, requiring less computation.

A single capsule is wired to represent a single entity, and its vector/matrix may learn to encode its pose w.r.t the coordinate frame imposed byanobserver.

When multiple predictions agree, a higher level capsule becomes active.

Capsule networks have recently gained a great deal of interest as a new architecture of neural networks that can be more robust to input perturbations than similar-sized CNNs.

Capsule networks are biologically inspired neural networks that group neurons into vectors called capsules, each explicitly representing an object or one of its parts. The routing mechanism connects capsules in consecutive layers, forming a hierarchical structure between parts and objects, also known as a parse tree. Capsule networks often attempt to model all elements in an image, requiring large network sizes to handle complexities such as intricate backgrounds or irrelevant objects. However, this comprehensive modeling leads to increased parameter counts and computational inefficiencies. Our goal is to enable capsule networks to focus only on the object of interest, reducing the number of parse trees. We accomplish this with REM (Routing Entropy Minimization), a technique that minimizes the entropy of the parse tree-like structure. REM drives the model parameters distribution towards low entropy configurations through a pruning mechanism, significantly reducing the generation of intra-class parse trees. This empowers capsules to learn more stable and succinct representations with fewer parameters and negligible performance loss.

Learning to infer object representations, and in particular part-whole hierarchies, has been the focus of extensive research in computer vision, in pursuit of improving data efficiency, systematic generalisation, and robustness. Models which are \emph{designed} to infer part-whole hierarchies, often referred to as capsule networks, are typically trained end-to-end on supervised tasks such as object classification, in which case it is difficult to evaluate whether such a model \emph{actually} learns to infer part-whole hierarchies, as claimed. To address this difficulty, we present a SYNthetic DAtaset for CApsule Testing and Evaluation, abbreviated as SynDaCaTE, and establish its utility by (1) demonstrating the precise bottleneck in a prominent existing capsule model, and (2) demonstrating that permutation-equivariant self-attention is highly effective for parts-to-wholes inference, which motivates future directions for designing effective inductive biases for computer vision.

Deep learning techniques are increasingly being adopted in diagnostic medical imaging. However, the limited availability of high-quality, large-scale medical datasets presents a significant challenge, often necessitating the use of transfer learning approaches. This study investigates self-supervised learning methods for pre-training capsule networks in polyp diagnostics for colon cancer. We used the PICCOLO dataset, comprising 3,433 samples, which exemplifies typical challenges in medical datasets: small size, class imbalance, and distribution shifts between data splits. Capsule networks offer inherent interpretability due to their architecture and inter-layer information routing mechanism. However, their limited native implementation in mainstream deep learning frameworks and the lack of pre-trained versions pose a significant challenge. This is particularly true if aiming to train them on small medical datasets, where leveraging pre-trained weights as initial parameters would be beneficial. We explored two auxiliary self-supervised learning tasks, colourisation and contrastive learning, for capsule network pre-training. We compared self-supervised pre-trained models against alternative initialisation strategies. Our findings suggest that contrastive learning and in-painting techniques are suitable auxiliary tasks for self-supervised learning in the medical domain. These techniques helped guide the model to capture important visual features that are beneficial for the downstream task of polyp classification, increasing its accuracy by 5.26% compared to other weight initialisation methods.

Post-rebuttal: I have considered the opinion and viewpoint of the other reviewers, who have both provided some good insight on the paper. I have also read the response of the authors very carefully, which has provided some more information. I am happy to revise my score reflecting the new evidence authors have provided. In that sense an expert is specialising in a different region of the input space, whose contributions are adjusted differently per example/input. What happens in the Dynamic Routing and EM is that the agreement between a higher level and lower level capsule is paramount for deciding if something is present in an image or which information to keep based on a voting process.

Brain tumors pose a serious health threat due to their rapid growth and potential for metastasis. While medical imaging has advanced significantly, accurately identifying and characterizing these tumors remains a challenge. This study addresses this challenge by leveraging the innovative TrAdaBoost methodology to enhance the Brain Tumor Segmentation (BraTS2020) dataset, aiming to improve the efficiency and accuracy of brain tumor classification. Our approach combines state-of-the-art deep learning algorithms, including the Vision Transformer (ViT), Capsule Neural Network (CapsNet), and convolutional neural networks (CNNs) such as ResNet-152 and VGG16. By integrating these models within a multi-classifier framework, we harness the strengths of each approach to achieve more robust and reliable tumor classification. A novel decision template is employed to synergistically combine outputs from different algorithms, further enhancing classification accuracy. To augment the training process, we incorporate a secondary dataset, "Brain Tumor MRI Dataset," as a source domain, providing additional data for model training and improving generalization capabilities. Our findings demonstrate a high accuracy rate in classifying tumor versus non-tumor images, signifying the effectiveness of our approach in the medical imaging domain. This study highlights the potential of advanced machine learning techniques to contribute significantly to the early and accurate diagnosis of brain tumors, ultimately improving patient outcomes.