Related papers: Current Symmetry Group Equivariant Convolution Fra…
Convolutional neural networks are ubiquitous in Machine Learning applications for solving a variety of problems. They however can not be used in their native form when the domain of the data is commonly encountered manifolds such as the…
Equivariance is a nice property to have as it produces much more parameter efficient neural architectures and preserves the structure of the input through the feature mapping. Even though some combinations of transformations might never…
Incorporating inductive bias by embedding geometric entities (such as rays) as input has proven successful in multi-view learning. However, the methods adopting this technique typically lack equivariance, which is crucial for effective 3D…
3D Euclidean symmetry equivariant neural networks have demonstrated notable success in modeling complex physical systems. We introduce a framework for relaxed $E(3)$ graph equivariant neural networks that can learn and represent symmetry…
Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…
Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…
Convolution is conventionally defined as a linear operation on functions of one or more variables which commutes with shifts. Group convolution generalizes the concept to linear operations on functions of group elements representing more…
The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…
Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and…
Convolution is an integral operation that defines how the shape of one function is modified by another function. This powerful concept forms the basis of hierarchical feature learning in deep neural networks. Although performing convolution…
The translational equivariant nature of Convolutional Neural Networks (CNNs) is a reason for its great success in computer vision. However, networks do not enjoy more general equivariance properties such as rotation or scaling, ultimately…
The notion of group invariance helps neural networks in recognizing patterns and features under geometric transformations. Group convolutional neural networks enhance traditional convolutional neural networks by incorporating group-based…
Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…
Categorical deep learning (CDL) has recently emerged as a framework that leverages category theory to unify diverse neural architectures. While geometric deep learning (GDL) is grounded in the specific context of invariants of group…
Interest has been rising lately towards methods representing data in non-Euclidean spaces, e.g. hyperbolic or spherical, that provide specific inductive biases useful for certain real-world data properties, e.g. scale-free, hierarchical or…
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…
Automatic tumor or lesion segmentation is a crucial step in medical image analysis for computer-aided diagnosis. Although the existing methods based on Convolutional Neural Networks (CNNs) have achieved the state-of-the-art performance,…
In recent years, supervised learning with convolutional networks (CNNs) has seen huge adoption in computer vision applications. Comparatively, unsupervised learning with CNNs has received less attention. In this work we hope to help bridge…
Equivariant machine learning methods have shown wide success at 3D learning applications in recent years. These models explicitly build in the reflection, translation and rotation symmetries of Euclidean space and have facilitated large…
Many classes of images exhibit rotational symmetry. Convolutional neural networks are sometimes trained using data augmentation to exploit this, but they are still required to learn the rotation equivariance properties from the data.…