Related papers: Lorentz-Equivariant Geometric Algebra Transformers…
Transfer learning is a crucial technique for handling a small amount of data that is potentially related to other abundant data. However, most of the existing methods are focused on classification tasks using images and language datasets.…
The Earth's subsurface is a cornerstone of modern society, providing essential energy resources like hydrocarbons, geothermal, and minerals while serving as the primary reservoir for $CO_2$ sequestration. However, full physics numerical…
Introducing prior auxiliary information from the knowledge graph (KG) to assist the user-item graph can improve the comprehensive performance of the recommender system. Many recent studies show that the ensemble properties of hyperbolic…
This paper presents GO-GAN, a novel Generative Adversarial Network (GAN) architecture for geometry optimization (GO), specifically to generate structures based on user-specified input parameters. The architecture for GO-GAN proposed here…
In this paper, we construct a single Lagrangian for both limits of Galilean electrodynamics. The framework relies on a covariant formalism used in describing Newton-Cartan geometry. We write down the Galilean conformal algebra and its…
The $D$-dimensional two-parameter deformed algebra with minimal length introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ($D+1$)-dimensional quantized space-time. For D=3, it includes Snyder algebra as a special…
We review the Inertial transformation and Lorentz transformation under a new context, by using Clifford Algebra or Geometric Algebra. The apparent contradiction between theses two approach is simply stems from different procedures for clock…
A deformation of the canonical algebra for kinematical observables of the quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistic invariant algebra obtained depends on…
This paper exploits Geometric (Clifford) Algebra (GA) theory in order to devise and introduce a new adaptive filtering strategy. From a least-squares cost function, the gradient is calculated following results from Geometric Calculus (GC),…
When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet…
This paper presents a new class of adaptive filters, namely Geometric-Algebra Adaptive Filters (GAAFs). They are generated by formulating the underlying minimization problem (a deterministic cost function) from the perspective of Geometric…
Relational Deep Learning (RDL) is a promising approach for building state-of-the-art predictive models on multi-table relational data by representing it as a heterogeneous temporal graph. However, commonly used Graph Neural Network models…
This paper explores the application of geometric algebra to Galilean spacetime and its physical implications. We introduce the Galilean Spacetime Algebra (GSTA), a five-dimensional conformal geometric algebra (CGA) generated by a specific…
Lorentz-equivariant neural networks are becoming the leading architectures for high-energy physics. Current implementations rely on specialized layers, limiting architectural choices. We introduce Lorentz Local Canonicalization (LLoCa), a…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…
Higher gauge theories play a prominent role in the construction of 4d topological invariants and have been long ago proposed as a tool for 4d quantum gravity. The Yetter lattice model and its continuum counterpart, the BFCG theory,…
Group equivariant neural networks are used as building blocks of group invariant neural networks, which have been shown to improve generalisation performance and data efficiency through principled parameter sharing. Such works have mostly…
Quantum computation represents an emerging framework to solve lattice gauge theories (LGT) with arbitrary gauge groups, a general and long-standing problem in computational physics. While quantum computers may encode LGT using only…
Learning a shared policy that guides the locomotion of different agents is of core interest in Reinforcement Learning (RL), which leads to the study of morphology-agnostic RL. However, existing benchmarks are highly restrictive in the…
Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes…