Related papers: Lorentz-Equivariant Geometric Algebra Transformers…

Equivariant network architectures are a well-established tool for predicting invariant or equivariant quantities. However, almost all learning problems considered in this context feature a global symmetry, i.e. each point of the underlying…

Lattice gas algorithms (LGA) are a class of algorithms including, in chronological order, binary lattice gas cellular automata (LGCA), integer lattice gas algorithms (ILGA) and lattice Boltzmann method (LBM). They are largely used for…

Graph Neural Networks (GNNs) have empowered the advance in graph-structured data analysis. Recently, the rise of Large Language Models (LLMs) like GPT-4 has heralded a new era in deep learning. However, their application to graph data poses…

Graph Convolutional Representation (GCR) has achieved impressive performance for graph data representation. However, existing GCR is generally defined on the input fixed graph which may restrict the representation capacity and also be…

Learning and reasoning about 3D molecular structures with varying size is an emerging and important challenge in machine learning and especially in drug discovery. Equivariant Graph Neural Networks (GNNs) can simultaneously leverage the…

Knowledge Graphs (KGs) are essential for the functionality of GraphRAGs, a form of Retrieval-Augmented Generative Systems (RAGs) that excel in tasks requiring structured reasoning and semantic understanding. However, creating KGs for…

Equivariant Graph Neural Networks (GNNs) are essential for physically consistent molecular simulations but suffer from high computational costs and memory bottlenecks, especially with high-order representations. While low-bit quantization…

Transformers are effective and efficient at modeling complex relationships and learning patterns from structured data in many applications. The main aim of this paper is to propose and design NLAFormer, which is a transformer-based…

This article shows that one can consistently incorporate nonunitary representations of at least one group into the ``ordinary'' nonrelativistic quantum mechanics. This group turns out to be Lorentz group thus giving us an alternative…

Transformers are very effective in capturing both global and local correlations within high-energy particle collisions, but they present deployment challenges in high-data-throughput environments, such as the CERN LHC. The quadratic…

Existing Graph Neural Networks (GNNs) compute the message exchange between nodes by either aggregating uniformly (convolving) the features of all the neighboring nodes, or by applying a non-uniform score (attending) to the features. Recent…

The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…

I tell about different mathematical tool that is important in general relativity. The text of the book includes definition of geometrical object, concept of reference frame, geometry of metric-affinne manifold. Using this concept I learn…

Machine learning algorithms are heavily relied on to understand the vast amounts of data from high-energy particle collisions at the CERN Large Hadron Collider (LHC). The data from such collision events can naturally be represented with…

This thesis deals with neural networks that respect symmetries and presents the advantages in applying them to lattice field theory problems. The concept of equivariance is explained, together with the reason why such a property is crucial…

Machine learning interatomic potentials trained on first-principles reference data are becoming valuable tools for computational physics, biology, and chemistry. Equivariant message-passing neural networks, including transformers, achieve…

In recent years, the use of machine learning has become increasingly popular in the context of lattice field theories. An essential element of such theories is represented by symmetries, whose inclusion in the neural network properties can…

Question Answering (QA) is a task that entails reasoning over natural language contexts, and many relevant works augment language models (LMs) with graph neural networks (GNNs) to encode the Knowledge Graph (KG) information. However, most…

In this paper we introduce concepts from relativity and geometric algebra to aeroacoustics. We do this using an acoustic space-time transformation within the framework of sound propagation in uniform flows. By using Geometric Algebra we are…

A program searching for symmetry structures behind some features of the standard Model is launched. After addressing known no-go theorems, we construct a novel symmetry mixing gauge and Higgs fields which is a Lorentz symmetry extension…