Related papers: Neural Group Actions
Data with geometric structure is ubiquitous in machine learning often arising from fundamental symmetries in a domain, such as permutation-invariance in graphs and translation-invariance in images. Group-convolutional architectures, which…
As generalizations of the original Volkov-Akulov action in four-dimensions, actions are found for all space-time dimensions D invariant under N non-linear realized global supersymmetries. We also give other such actions invariant under the…
The complete classification of the irreducible representations of the N-extended one-dimensional supersymmetry algebra linearly realized on a finite number of fields is presented. Off-shell invariant actions of one-dimensional…
Active solids, more specifically elastic lattices embedded with polar active units, exhibit collective actuation when the elasto-active feedback, generically present in such systems, exceeds some critical value. The dynamics then…
Quantum algorithms for factoring and discrete logarithm have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden…
An action of a group on a vector space partitions the latter into a set of orbits. We consider three natural and useful algorithmic "isomorphism" or "classification" problems, namely, orbit equality, orbit closure intersection, and orbit…
We establish rigidity for partial transformation groupoids associated with algebraic actions of semigroups: If two such groupoids (satisfying appropriate conditions) are isomorphic, then the globalizations of the initial algebraic actions…
We propose a novel approach to addressing the vanishing (or exploding) gradient problem in deep neural networks. We construct a new architecture for deep neural networks where all layers (except the output layer) of the network are a…
This article explores the novel notion of gyrogroup actions, which is a natural generalization of the usual notion of group actions. As a first step toward the study of gyrogroup actions from the algebraic viewpoint, we prove three…
In the framework of quantum group theory we obtain a noncommutative analog for the algebra of functions in a bounded symmetric domain, endowed with a whole symmetry. Also we provide a construction for its faithfull irreducible…
We present a neural network architecture, Bispectral Neural Networks (BNNs) for learning representations that are invariant to the actions of compact commutative groups on the space over which a signal is defined. The model incorporates the…
In this article, we generalise Haglund and Wise's theory of special cube complexes to groups acting on quasi-median graphs. More precisely, we define special actions on quasi-median graphs, and we show that a group which acts specially on a…
A generalization of G-sets, called partial G-sets, are the sets that admit an action of partial maps on their subsets. Partial actions are a powerful tool to generalize many results of group actions. These generalizations are obtained by…
Numerous invariant (or equivariant) neural networks have succeeded in handling invariant data such as point clouds and graphs. However, a generalization theory for the neural networks has not been well developed, because several essential…
In 2000, M. Burger and S. Mozes introduced universal groups acting on trees with a prescribed local action. We generalize this concept to groups acting on right-angled buildings. When the right-angled building is thick and irreducible of…
The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models. For example, group equivariant neural networks have…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
The universal approximation theorem is generalised to uniform convergence on the (noncompact) input space $\mathbb{R}^n$. All continuous functions that vanish at infinity can be uniformly approximated by neural networks with one hidden…
Recently, it was proved that group equivariance emerges in ensembles of neural networks as the result of full augmentation in the limit of infinitely wide neural networks (neural tangent kernel limit). In this paper, we extend this result…
We develop a learning-based algorithm for the distributed formation control of networked multi-agent systems governed by unknown, nonlinear dynamics. Most existing algorithms either assume certain parametric forms for the unknown dynamic…