Related papers: Recognising the small Ree groups in their natural …

Constructive algorithms, requiring no more than $2\times 2$ matrix manipulations, are provided for finding the entries of the positive definite factor in the polar decomposition of matrices in sixteen groups preserving a bilinear form in…

Recent advances in generative models have highlighted the need for robust detectors capable of distinguishing real images from AI-generated images. While existing methods perform well on known generators, their performance often declines…

We study the natural gradient method for learning in deep Bayesian networks, including neural networks. There are two natural geometries associated with such learning systems consisting of visible and hidden units. One geometry is related…

Neural Architecture Search (NAS) methods have been successfully applied to image tasks with excellent results. However, NAS methods are often complex and tend to converge to local minima as soon as generated architectures seem to yield good…

Retriever-augmented generation (RAG) has become a widely adopted approach for enhancing the factual accuracy of large language models (LLMs). While current benchmarks evaluate the performance of RAG methods from various perspectives, they…

In this paper, we study the problem of structure learning for Bayesian networks in which nodes take discrete values. The problem is NP-hard in general but we show that under certain conditions we can recover the true structure of a Bayesian…

Several causal discovery algorithms have been proposed. However, when the sample size is small relative to the number of variables, the accuracy of estimating causal graphs using existing methods decreases. And some methods are not feasible…

We describe a family of new algorithms for finding the canonical image of a set of points under the action of a permutation group. This family of algorithms makes use of the orbit structure of the group, and a chain of subgroups of the…

We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…

Algorithmic self-assembly, a generalization of crystal growth processes, has been proposed as a mechanism for autonomous DNA computation and for bottom-up fabrication of complex nanostructures. A `program' for growing a desired structure…

Despite the success of generative adversarial networks (GANs) in generating visually appealing images, they are notoriously challenging to train. In order to stabilize the learning dynamics in minimax games, we propose a novel recursive…

In the article, we discuss the architecture of the polynomial neural network that corresponds to the matrix representation of Lie transform. The matrix form of Lie transform is an approximation of the general solution of the nonlinear…

We propose a new construction of two-dimensional natural bi-Hamiltonian systems associated with a very simple Lie algebra. The presented construction allows us to distinguish three families of super-integrable monomial potentials for which…

A numerical algorithm that computes the decomposition of any finite-dimen\-sio\-nal unitary reducible representation of a compact Lie group is presented. The algorithm, which does not rely on an algebraic insight on the group structure, is…

This work represents a natural coalescence of two important lines of work: learning mixtures of Gaussians and algorithmic robust statistics. In particular we give the first provably robust algorithm for learning mixtures of any constant…

Reinforcement learning (RL) has proven itself as a powerful tool for the discovery of quantum circuits and quantum protocols. We have recently shown that including composite quantum gates -- referred to as ``gadgets'' -- in the action space…

The decomposition of complex structures into simpler substructures is a powerful technique with a wide range of applications. We study the computation of decompositions in the context of programmable matter. The amoebot model is a…

We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure,…

We describe several additions to the ENIGMA system that guides clause selection in the E automated theorem prover. First, we significantly speed up its neural guidance by adding server-based GPU evaluation. The second addition is motivated…

RIPE is a novel deterministic and easily understandable prediction algorithm developed for continuous and discrete ordered data. It infers a model, from a sample, to predict and to explain a real variable $Y$ given an input variable $X \in…