相关论文: Some new methods to build group equivariant non-ex…

Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we…

We introduce steerable neural ordinary differential equations on homogeneous spaces $M=G/H$. These models constitute a novel geometric extension of manifold neural ordinary differential equations (NODEs) that transport associated feature…

Gauge-invariant quantum fields are constructed in an Abelian power-counting renormalizable gauge theory with both scalar, vector and fermionic matter content. This extends previous results already obtained for the gauge-invariant…

Let $\gp$ be a finite group acting on a compact manifold $M$ and $\maA(M)$ denote the algebra of classical complete symbols on $M$. We determine all traces on the cross-product algebra $\maA(M) \rtimes \Gamma$. These traces appear as…

Several recent papers have proposed increasing the expressive power of graph neural networks by exploiting subgraphs or other topological structures. In parallel, researchers have investigated higher order permutation equivariant networks.…

Neural operators offer powerful approaches for solving parametric partial differential equations, but extending them to spherical domains remains challenging due to the need to preserve intrinsic geometry while avoiding distortions that…

It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of…

This paper is devoted to the study of geometric structures modeled on homogeneous spaces G/P, where G is a real or complex semisimple Lie group and $P\subset G$ is a parabolic subgroup. We use methods from differential geometry and very…

As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…

Generative models rely on the key idea that data can be represented in terms of latent variables which are uncorrelated by definition. Lack of correlation is important because it suggests that the latent space manifold is simpler to…

In many applications concerning the comparison of data expressed by $\mathbb{R}^m$-valued functions defined on a topological space $X$, the invariance with respect to a given group $G$ of self-homeomorphisms of $X$ is required. While…

We introduce a practical construction of group-equivariant and permutation-invariant functions of $N$ variables given a finite-dimensional space stable with respect to the group action. The construction applies to any connected linear Lie…

Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these…

The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…

We prove a number of results to the effect that generic quantum graphs (defined via operator systems as in the work of Duan-Severini-Winter / Weaver) have few symmetries: for a Zariski-dense open set of tuples $(X_1,\cdots,X_d)$ of…

This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…

J. Pevtsova and the author constructed a ``universal $p$-nilpotent operator" for an infinitesimal group scheme $G$ over a field $k$ of characteristic $p > 0$ which led to coherent sheaves on the scheme of 1-parameter subgroups of $G$…

In this paper we study the discrete-time dynamical systems associated with gonosomal algebras used as algebraic model in the sex-linked genes inheritance. We show that the class of gonosomal algebras is disjoint from the other…

In recent years, tasks of machine learning ranging from image processing & audio/video analysis to natural language understanding have been transformed by deep learning. The data content in all these scenarios are expressed via Euclidean…

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…