Related papers: Discovering Sparse Representations of Lie Groups w…

We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…

Sparse coding strategies have been lauded for their parsimonious representations of data that leverage low dimensional structure. However, inference of these codes typically relies on an optimization procedure with poor computational…

We suggest a new algorithm to estimate representations of compact Lie groups from finite samples of their orbits. Different from other reported techniques, our method allows the retrieval of the precise representation type as a direct sum…

Supervised learning has become a cornerstone of modern machine learning, yet a comprehensive theory explaining its effectiveness remains elusive. Empirical phenomena, such as neural analogy-making and the linear representation hypothesis,…

This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that…

The interest of the deep learning community in image synthesis has grown massively in recent years. Nowadays, deep generative methods, and especially Generative Adversarial Networks (GANs), are leading to state-of-the-art performance,…

Orthosymplectic Lie superalgebras are fundamental symmetries in modern physics, such as massive supergravity. However, their representations are far from being thoroughly understood. In the present paper, we completely determine the…

Learned sparse and dense representations capture different successful approaches to text retrieval and the fusion of their results has proven to be more effective and robust. Prior work combines dense and sparse retrievers by fusing their…

We show how fitting sparse linear models over learned deep feature representations can lead to more debuggable neural networks. These networks remain highly accurate while also being more amenable to human interpretation, as we demonstrate…

An ability to model a generative process and learn a latent representation for speech in an unsupervised fashion will be crucial to process vast quantities of unlabelled speech data. Recently, deep probabilistic generative models such as…

Deep latent variable models are powerful tools for representation learning. In this paper, we adopt the deep information bottleneck model, identify its shortcomings and propose a model that circumvents them. To this end, we apply a copula…

We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.

A method to construct in explicit form the generators of the simple roots of an arbitrary finite-dimensional representation of a quantum or standard semisimple algebra is found. The method is based on general results from the global theory…

For a semisimple Lie group $G$, we study Discrete Series representations with admissible branching to a symmetric subgroup $H$. This is done using a canonical associated symmetric subgroup $H_0$, forming a pseudo-dual pair with $H$, and a…

The main purpose of this paper is providing a simple method to generate the matrices of irreducible representations because it is useful to reduce the computational time of solving the eigenvalue problems. The only information we need to…

We propose a method to facilitate exploration and analysis of new large data sets. In particular, we give an unsupervised deep learning approach to learning a latent representation that captures semantic similarity in the data set. The core…

We introduce an explainable generative model by applying sparse operation on the feature maps of the generator network. Meaningful hierarchical representations are obtained using the proposed generative model with sparse activations. The…

Recent work has constructed neural networks that are equivariant to continuous symmetry groups such as 2D and 3D rotations. This is accomplished using explicit Lie group representations to derive the equivariant kernels and nonlinearities.…

Deep convolutional networks (convnets) show a remarkable ability to learn disentangled representations. In recent years, the generalization of deep learning to Lie groups beyond rigid motion in $\mathbb{R}^n$ has allowed to build convnets…

We present a finite algorithm for computing the set of irreducible unitary representations of a real reductive group G. The Langlands classification, as formulated by Knapp and Zuckerman, exhibits any representation with an invariant…