Related papers: Building Deep, Equivariant Capsule Networks

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…

Convolutional neural networks revolutionized computer vision and natrual language processing. Their efficiency, as compared to fully connected neural networks, has its origin in the architecture, where convolutions reflect the translation…

We present a framework to use recently introduced Capsule Networks for solving the problem of Optical Flow, one of the fundamental computer vision tasks. Most of the existing state of the art deep architectures either uses a correlation…

Analyzing scalar and vector fields on the sphere, such as temperature or wind speed and direction on Earth, is a difficult task. Models should respect both the rotational symmetries of the sphere and the inherent symmetries of the vector…

Capsule networks (CapsNets) aim to parse images into a hierarchy of objects, parts, and their relations using a two-step process involving part-whole transformation and hierarchical component routing. However, this hierarchical relationship…

Machine learning based methods achieves impressive results in object classification and detection. Utilizing representative data of the visual world during the training phase is crucial to achieve good performance with such data driven…

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…

The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…

Deep learning for predicting the electronic-structure Hamiltonian of quantum systems necessitates satisfying the covariance laws, among which achieving SO(3)-equivariance without sacrificing the non-linear expressive capability of networks…

Capsule networks(CapsNet) are recently proposed neural network models with new processing layers, specifically for entity representation and discovery of images. It is well known that CapsNet have some advantages over traditional neural…

Capsule networks are a neural network architecture specialized for visual scene recognition. Features and pose information are extracted from a scene and then dynamically routed through a hierarchy of vector-valued nodes called 'capsules'…

Past few years have witnessed exponential growth of interest in deep learning methodologies with rapidly improving accuracies and reduced computational complexity. In particular, architectures using Convolutional Neural Networks (CNNs) have…

Many learning tasks, including learning potential energy surfaces from ab initio calculations, involve global spatial symmetries and permutational symmetry between atoms or general particles. Equivariant graph neural networks are a standard…

Training a Convolutional Neural Network (CNN) to be robust against rotation has mostly been done with data augmentation. In this paper, another progressive vision of research direction is highlighted to encourage less dependence on data…

Equivariant networks are specifically designed to ensure consistent behavior with respect to a set of input transformations, leading to higher sample efficiency and more accurate and robust predictions. However, redesigning each component…

In recent years, convolutional neural networks (CNN) have played an important role in the field of deep learning. Variants of CNN's have proven to be very successful in classification tasks across different domains. However, there are two…

Although provably robust to translational perturbations, convolutional neural networks (CNNs) are known to suffer from extreme performance degradation when presented at test time with more general geometric transformations of inputs.…

Recent advances in deep learning and Transformers have driven major breakthroughs in robotics by employing techniques such as imitation learning, reinforcement learning, and LLM-based multimodal perception and decision-making. However,…

Equivariant neural networks provide a principled framework for incorporating symmetry into learning architectures and have been extensively analyzed through the lens of their separation power, that is, the ability to distinguish inputs…

Building on recent work on capsule networks, we propose a new, general-purpose form of "routing by agreement" that activates output capsules in a layer as a function of their net benefit to use and net cost to ignore input capsules from…