Related papers: Symmetry Group Equivariant Architectures for Physi…
High-performance machine learning tools in particle physics rest on two complementary directions: encoding symmetries explicitly in the architecture, and implicitly learning the structure of the data through large-scale (pre-) training. We…
Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable at present on classical architectures. Here, we discuss…
Noncommutative geometry has seen remarkable applications for high energy physics, viz. the geometrical interpretation of the Standard Model. The question whether it also allows for supersymmetric theories has so far not been answered in a…
Physical properties of matter are tightly related with the kind of symmetry of the medium. Group theory is a systematic tool, though not always easy to handle, to exploit symmetry properties, for instance to find the eigenvectors and…
Machine learning (ML) provides a broad spectrum of tools and architectures that enable the transformation of data from simulations and experiments into useful and explainable science, thereby augmenting domain knowledge. Furthermore,…
We consider achieving equivariance in machine learning systems via frame averaging. Current frame averaging methods involve a costly sum over large frames or rely on sampling-based approaches that only yield approximate equivariance. Here,…
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…
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…
Real-world robotic applications, from autonomous exploration to assistive technologies, require adaptive, interpretable, and data-efficient learning paradigms. While deep learning architectures and foundation models have driven significant…
This presentation explains why models with a dynamical symmetry often work extraordinarily well even in the presence of large symmetry breaking interactions. A model may be a caricature of a more realistic system with a "quasi-dynamical"…
Embodied systems experience the world as 'a symphony of flows': a combination of many continuous streams of sensory input coupled to self-motion, interwoven with the dynamics of external objects. These streams obey smooth,…
Many classes of images exhibit rotational symmetry. Convolutional neural networks are sometimes trained using data augmentation to exploit this, but they are still required to learn the rotation equivariance properties from the data.…
Symmetry learning has proven to be an effective approach for extracting the hidden structure of data, with the concept of equivariance relation playing the central role. However, most of the current studies are built on architectural theory…
The implementation of physical symmetries into problem descriptions allows for the reduction of parameters and computational complexity. We show the integration of the permutation symmetry as the most restrictive discrete symmetry into…
Inspired by constraints from physical law, equivariant machine learning restricts the learning to a hypothesis class where all the functions are equivariant with respect to some group action. Irreducible representations or invariant theory…
Methods for the design of physical parameterization schemes that possess certain invariance properties are discussed. These methods are based on different techniques of group classification and provide means to determine expressions for…
Quantum Machine Learning (QML) models are aimed at learning from data encoded in quantum states. Recently, it has been shown that models with little to no inductive biases (i.e., with no assumptions about the problem embedded in the model)…
In certain situations, neural networks are trained upon data that obey underlying symmetries. However, the predictions do not respect the symmetries exactly unless embedded in the network structure. In this work, we introduce architectures…
Electromagnetic (EM) imaging is widely applied in sensing for security, biomedicine, geophysics, and various industries. It is an ill-posed inverse problem whose solution is usually computationally expensive. Machine learning (ML)…