Related papers: A Practical Method for Constructing Equivariant Mu…

Matrix manifolds, such as manifolds of Symmetric Positive Definite (SPD) matrices and Grassmann manifolds, appear in many applications. Recently, by applying the theory of gyrogroups and gyrovector spaces that is a powerful framework for…

Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…

Equivariant networks have been adopted in many 3-D learning areas. Here we identify a fundamental limitation of these networks: their ambiguity to symmetries. Equivariant networks cannot complete symmetry-dependent tasks like segmenting a…

Geometric quantum machine learning uses the symmetries inherent in data to design tailored machine learning tasks with reduced search space dimension. The field has been well-studied recently in an effort to avoid barren plateau issues…

We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…

Optimizing and certifying the positivity of polynomials are fundamental primitives across mathematics and engineering applications, from dynamical systems to operations research. However, solving these problems in practice requires large…

Pixelizations of Platonic solids such as the cube and icosahedron have been widely used to represent spherical data, from climate records to Cosmic Microwave Background maps. Platonic solids have well-known global symmetries. Once we…

We prove an impossibility result, which in the context of function learning says the following: under certain conditions, it is impossible to simultaneously learn symmetries and functions equivariant under them using an ansatz consisting of…

The convolutional layers of standard convolutional neural networks (CNNs) are equivariant to translation. However, the convolution and fully-connected layers are not equivariant or invariant to other affine geometric transformations.…

We introduce the usage of equivariant neural networks in the search for violations of the charge-parity ($\textit{CP}$) symmetry in particle interactions at the CERN Large Hadron Collider. We design neural networks that take as inputs…

Robotic manipulation systems are increasingly deployed across diverse domains. Yet existing multi-modal learning frameworks lack inherent guarantees of geometric consistency, struggling to handle spatial transformations such as rotations…

We introduce a novel co-learning paradigm for manifolds naturally equipped with a group action, motivated by recent developments on learning a manifold from attached fibre bundle structures. We utilize a representation theoretic mechanism…

The crucial role played by the underlying symmetries of high energy physics and lattice field theories calls for the implementation of such symmetries in the neural network architectures that are applied to the physical system under…

Graph machine learning architectures are typically tailored to specific tasks on specific datasets, which hinders their broader applicability. This has led to a new quest in graph machine learning: how to build graph foundation models…

We investigate the relation between end-to-end equivariance and layerwise equivariance in deep neural networks. We prove the following: For a network whose end-to-end function is equivariant with respect to group actions on the input and…

Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…

Graph neural networks (GNNs) have become a core paradigm for learning on relational data. In materials science, equivariant GNNs (EGNNs) have emerged as a compelling backbone for crystalline-structure prediction, owing to their ability to…

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…

Equivariance to permutations and rigid motions is an important inductive bias for various 3D learning problems. Recently it has been shown that the equivariant Tensor Field Network architecture is universal -- it can approximate any…

Augmentation-based self-supervised learning methods have shown remarkable success in self-supervised visual representation learning, excelling in learning invariant features but often neglecting equivariant ones. This limitation reduces the…