Related papers: Equivariant Spherical Transformer for Efficient Mo…

The Symmetric group $S_{n}$ manifests itself in large classes of quantum systems as the invariance of certain characteristics of a quantum state with respect to permuting the qubits. The subgroups of $S_{n}$ arise, among many other…

Neural networks are a promising tool for simulating quantum many body systems. Recently, it has been shown that neural network-based models describe quantum many body systems more accurately when they are constrained to have the correct…

Message passing neural networks have become a method of choice for learning on graphs, in particular the prediction of chemical properties and the acceleration of molecular dynamics studies. While they readily scale to large training data…

Neuromorphic computing has emerged as a promising energy-efficient alternative to traditional artificial intelligence, predominantly utilizing spiking neural networks (SNNs) implemented on neuromorphic hardware. Significant advancements…

We introduce Equivariant Neural Field Expectation Maximization (EFEM), a simple, effective, and robust geometric algorithm that can segment objects in 3D scenes without annotations or training on scenes. We achieve such unsupervised…

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…

We present e3nn, a generalized framework for creating E(3) equivariant trainable functions, also known as Euclidean neural networks. e3nn naturally operates on geometry and geometric tensors that describe systems in 3D and transform…

Soft, porous mechanical metamaterials exhibit pattern transformations that may have important applications in soft robotics, sound reduction and biomedicine. To design these innovative materials, it is important to be able to simulate them…

Equivariant Graph neural Networks (EGNs) are powerful in characterizing the dynamics of multi-body physical systems. Existing EGNs conduct flat message passing, which, yet, is unable to capture the spatial/dynamical hierarchy for complex…

Predicting low-energy molecular conformations given a molecular graph is an important but challenging task in computational drug discovery. Existing state-of-the-art approaches either resort to large scale transformer-based models that…

Wavelet scattering networks, which are convolutional neural networks (CNNs) with fixed filters and weights, are promising tools for image analysis. Imposing symmetry on image statistics can improve human interpretability, aid in…

Equivariant Graph Neural Networks (GNNs) have achieved remarkable success across diverse scientific applications. However, existing approaches face critical efficiency challenges when scaling to large geometric graphs and suffer significant…

Modeling molecular potential energy surface is of pivotal importance in science. Graph Neural Networks have shown great success in this field. However, their message passing schemes need special designs to capture geometric information and…

Transformation Equivariant Representations (TERs) aim to capture the intrinsic visual structures that equivary to various transformations by expanding the notion of {\em translation} equivariance underlying the success of Convolutional…

Graph Neural Networks (GNNs) with equivariant properties have achieved significant success in modeling complex dynamic systems and molecular properties. However, their expressiveness ability is limited by: (1) Existing methods often…

Neural Functional Networks (NFNs) have gained increasing interest due to their wide range of applications, including extracting information from implicit representations of data, editing network weights, and evaluating policies. A key…

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…

Circuit representation learning has shown promising results in advancing the field of Electronic Design Automation (EDA). Existing models, such as DeepGate Family, primarily utilize Graph Neural Networks (GNNs) to encode circuit netlists…

Multi-frequency Electrical Impedance Tomography (mfEIT) represents a promising biomedical imaging modality that enables the estimation of tissue conductivities across a range of frequencies. Addressing this challenge, we present a novel…

Despite recent advancement in 3D molecule conformation generation driven by diffusion models, its high computational cost in iterative diffusion/denoising process limits its application. In this paper, an equivariant consistency model…