Related papers: Group Equivariant Capsule Networks

Learning from set-structured data, such as point clouds, has gained significant attention from the machine learning community. Geometric deep learning provides a blueprint for designing effective set neural networks that preserve the…

The difficult problem of relating the static structure of glassy liquids and their dynamics is a good target for Machine Learning, an approach which excels at finding complex patterns hidden in data. Indeed, this approach is currently a hot…

Capsule networks are a type of neural network that have recently gained increased popularity. They consist of groups of neurons, called capsules, which encode properties of objects or object parts. The connections between capsules encrypt…

In this paper we introduce a new inductive bias for capsule networks and call networks that use this prior $\gamma$-capsule networks. Our inductive bias that is inspired by TE neurons of the inferior temporal cortex increases the…

Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However,…

Rotation-invariance is a desired property of machine-learning models for medical image analysis and in particular for computational pathology applications. We propose a framework to encode the geometric structure of the special Euclidean…

The group invariance of entanglement is obtained within a very general and simple setup of the latter, given by a recently introduced considerably extended concept of tensor products. This general approach to entanglement - unlike the usual…

Recordings of increasingly large neural populations have revealed that the firing of individual neurons is highly coordinated. When viewed in the space of all possible patterns, the collective activity forms non-linear structures called…

We construct and evaluate group-equivariant neural networks for the prediction of the two-dimensional $Q$-tensor order parameter of nematic liquid crystals from synthetically generated microscopic textures. Seven architectures, equivariant…

A formal description of the compositionality of neural networks is associated directly with the formal grammar-structure of the objects it seeks to represent. This formal grammar-structure specifies the kind of components that make up an…

Symmetry-aware architectures are central to geometric deep learning. We present a systematic approach for constructing continuous rotationally invariant and equivariant functions using symmetric tensor networks. The proposed framework…

Graph Neural Networks (GNN) come in many flavors, but should always be either invariant (permutation of the nodes of the input graph does not affect the output) or equivariant (permutation of the input permutes the output). In this paper,…

The inclusion of symmetries as an inductive bias, known as equivariance, often improves generalization on geometric data (e.g. grids, sets, and graphs). However, equivariant architectures are usually highly constrained, designed for…

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…

In the recent application of scientific modeling, machine learning models are largely applied to facilitate computational simulations of fluid systems. Rotation symmetry is a general property for most symmetric fluid systems. However, in…

The study of $G$-equivariant operators is of great interest to explain and understand the architecture of neural networks. In this paper we show that each linear $G$-equivariant operator can be produced by a suitable permutant measure,…

Capsule networks use routing algorithms to flow information between consecutive layers. In the existing routing procedures, capsules produce predictions (termed votes) for capsules of the next layer. In a nutshell, the next-layer capsule's…

Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…

We develop a theory of category-equivariant neural networks (CENNs) that unifies group/groupoid-equivariant networks, poset/lattice-equivariant networks, graph and sheaf neural networks. Equivariance is formulated as naturality in a…

Recent foundational models for tabular data, such as TabPFN, excel at adapting to new tasks via in-context learning, but remain constrained to a fixed, pre-defined number of target dimensions-often necessitating costly ensembling…