Related papers: Equivariant Transformer is all you need
Machine learning and deep learning have revolutionized computational physics, particularly the simulation of complex systems. Equivariance is essential for simulating physical systems because it imposes a strong inductive bias on the…
Using symmetry as an inductive bias in deep learning has been proven to be a principled approach for sample-efficient model design. However, the relationship between symmetry and the imperative for equivariance in neural networks is not…
Extensive work has demonstrated that equivariant neural networks can significantly improve sample efficiency and generalization by enforcing an inductive bias in the network architecture. These applications typically assume that the domain…
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…
Machine-learning (ML) ans\"atze have greatly expanded the accuracy and reach of variational quantum Monte Carlo (QMC) calculations, in particular when exploring the manifold quantum phenomena exhibited by spin systems. However, the…
The rising adoption of machine learning in high energy physics and lattice field theory necessitates the re-evaluation of common methods that are widely used in computer vision, which, when applied to problems in physics, can lead to…
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…
From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…
The requirement of generating predictions that exactly fulfill the fundamental symmetry of the corresponding physical quantities has profoundly shaped the development of machine-learning models for physical simulations. In many cases,…
Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to…
Complex spin-spin interactions in magnets can often lead to magnetic superlattices with complex local magnetic arrangements, and many of the magnetic superlattices have been found to possess non-trivial topological electronic properties.…
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…
Group equivariance has emerged as a valuable inductive bias in deep learning, enhancing generalization, data efficiency, and robustness. Classically, group equivariant methods require the groups of interest to be known beforehand, which may…
Machine-learning (ML) force fields enable large-scale simulations with near-first-principles accuracy at substantially reduced computational cost. Recent work has extended ML force-field approaches to adiabatic dynamical simulations of…
In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency. While…
Shift equivariance is a fundamental principle that governs how we perceive the world - our recognition of an object remains invariant with respect to shifts. Transformers have gained immense popularity due to their effectiveness in both…
In machine learning datasets with symmetries, the paradigm for backward compatibility with symmetry-breaking has been to relax equivariant architectural constraints, engineering extra weights to differentiate symmetries of interest.…
Equivariance to symmetries has proven to be a powerful inductive bias in deep learning research. Recent works on mesh processing have concentrated on various kinds of natural symmetries, including translations, rotations, scaling, node…
State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…
Equivariant neural networks are designed to respect symmetries through their architecture, boosting generalization and sample efficiency when those symmetries are present in the data distribution. Real-world data, however, often departs…