Related papers: Discovering Sparse Representations of Lie Groups w…
Semantic segmentation with Convolutional Neural Networks is a memory-intensive task due to the high spatial resolution of feature maps and output predictions. In this paper, we present Quadtree Generating Networks (QGNs), a novel approach…
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…
Identifying damage of structural systems is typically characterized as an inverse problem which might be ill-conditioned due to aleatory and epistemic uncertainties induced by measurement noise and modeling error. Sparse representation can…
We establish some results about large restricted Lie algebras similar to those known in the Group Theory. As an application we use this group-theoretic approach to produce some examples of restricted as well as ordinary Lie algebras which…
A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks that are complicated by nuisance variation. For instance, visual object recognition involves…
Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning. Both pursuits require knowledge of the underlying symmetries in data, yet discovering these symmetries…
Matrix generators for the general and special linear groups, the symplectic groups and the general and special unitary groups over finite fields. For the most part the generators have been obtained by translating Steinberg's generators for…
A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. The method is illustrated by an example. We also discuss an implementation of the algorithm in the language of the…
Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the…
We introduce a new approach to learning in hierarchical latent-variable generative models called the "distributed distributional code Helmholtz machine", which emphasises flexibility and accuracy in the inferential process. In common with…
Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
In this paper we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps. In particular, a few classical results of Steinberg and Deligne & Lusztig on complex representations of finite…
Sparse coding algorithm is an learning algorithm mainly for unsupervised feature for finding succinct, a little above high - level Representation of inputs, and it has successfully given a way for Deep learning. Our objective is to use High…
In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using difference operators. The operators are…
L\'evy processes on bialgebras are families of infinitely divisible representations. We classify the generators of L\'evy processes on the compact forms of the quantum algebras $U_q(g)$, where $g$ is a simple Lie algebra. Then we show how…
In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies,…
We present a method for feature interpretation that makes use of recent advances in autoregressive density estimation models to invert model representations. We train generative inversion models to express a distribution over input features…
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
In this article we present a new C*-algebraic deformation of the Lorentz group. It is obtained by means of the Rieffel deformation applied to SL(2,C). We give a detailed description of the resulting quantum group in terms of generators -…