Related papers: A Single Architecture for Representing Invariance …
In this work, we formally prove that, under certain conditions, if a neural network is invariant to a finite group then its weights recover the Fourier transform on that group. This provides a mathematical explanation for the emergence of…
Accurate simulations of atomistic systems from first principles are limited by computational cost. In high-throughput settings, machine learning can reduce these costs significantly by accurately interpolating between reference…
We have developed a symmetry-adapted modeling procedure for molecules and crystals. By using the completeness of multipoles to express spatial and time-reversal parity-specific anisotropic distributions, we can generate systematically the…
The dictionary learning problem concerns the task of representing data as sparse linear sums drawn from a smaller collection of basic building blocks. In application domains where such techniques are deployed, we frequently encounter…
Crystallographic symmetry classifications from real-world images with periodicities in two dimensions (2D) are of interest to crystallographers and practitioners of computer vision studies alike. Currently, these classifications are…
Machine learning has made important headway in helping to improve the treatment of quantum many-body systems. A domain of particular relevance are correlated inhomogeneous systems. What has been missing so far is a general, scalable…
Symmetry packaging is the phenomenon whereby, upon particle creation, all the internal quantum numbers (IQNs) become locked into a single irreducible representation (irrep) block of the gauge group, as required by locality and gauge…
Crystal structures are defined by the periodic arrangement of atoms in 3D space, inherently making them equivariant to SO(3) group. A fundamental requirement for crystal property prediction is that the model's output should remain invariant…
Unlike image or text domains that benefit from an abundance of large-scale datasets, point cloud learning techniques frequently encounter limitations due to the scarcity of extensive datasets. To overcome this limitation, we present…
Symmetry arises often when learning from high dimensional data. For example, data sets consisting of point clouds, graphs, and unordered sets appear routinely in contemporary applications, and exhibit rich underlying symmetries.…
We present detailed elaboration and first generally applicable linearization routines of the \textit{Parameter Space Concept} (PSC) for determining 1-dimensionally projected structures of $m$ independent scatterers. This crystal…
Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in…
Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…
Spatial symmetries and invariances play an important role in the behaviour of materials and should be respected in the description and modelling of material properties. The focus here is the class of physically symmetric and positive…
This paper presents a series of general results about the optimal estimation of physical transformations in a given symmetry group. In particular, it is shown how the different symmetries of the problem determine different properties of the…
Although learning in high dimensions is commonly believed to suffer from the curse of dimensionality, modern machine learning methods often exhibit an astonishing power to tackle a wide range of challenging real-world learning problems…
Symmetry, a central concept in understanding the laws of nature, has been used for centuries in physics, mathematics, and chemistry, to help make mathematical models tractable. Yet, despite its power, symmetry has not been used extensively…
The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks…
Learning distance functions between complex objects, such as the Wasserstein distance to compare point sets, is a common goal in machine learning applications. However, functions on such complex objects (e.g., point sets and graphs) are…
Incorporating group symmetries into neural networks has been a cornerstone of success in many AI-for-science applications. Diagonal groups of isometries, which describe the invariance under a simultaneous movement of multiple objects, arise…