Related papers: Mathematical conjecture generation using machine i…

When multitudes of features can plausibly be associated with a response, both privacy considerations and model parsimony suggest grouping them to increase the predictive power of a regression model. Specifically, the identification of…

We use a large census of hyperbolic 3-manifolds to experimentally investigate a conjecture of Neumann regarding the Bloch Group. We present an augmented census including, for feasible invariant trace fields, explicit manifolds (associated…

Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…

Distinguishing between real and AI-generated images, commonly referred to as 'image detection', presents a timely and significant challenge. Despite extensive research in the (semi-)supervised regime, zero-shot and few-shot solutions have…

We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that…

Unsupervised domain mapping has attracted substantial attention in recent years due to the success of models based on the cycle-consistency assumption. These models map between two domains by fooling a probabilistic discriminator, thereby…

It is shown here how prior estimates on the local shape of the universe can be used to reduce, to a small region, the full parameter space for the search of circles in the sky. This is the first step towards the development of efficient…

Previous work has suggested that the structural restrictions of graphs from classes of bounded expansion--locally dense pockets in a globally sparse graph--naturally coincide with common properties of real-world networks such as clustering…

Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…

It has long been thought that high-dimensional data encountered in many practical machine learning tasks have low-dimensional structure, i.e., the manifold hypothesis holds. A natural question, thus, is to estimate the intrinsic dimension…

Graph Neural Networks (GNN) provide a powerful framework that elegantly integrates Graph theory with Machine learning for modeling and analysis of networked data. We consider the problem of quantifying the uncertainty in predictions of GNN…

Following an idea of Rowland we give a conjectural way to generate increasing sequences of primes using algorithms involving the gcd. These algorithms seem not so useless for searching primes since it appears we found sometime primes much…

This work focuses on designing a pipeline for the prediction of bankruptcy. The presence of missing values, high dimensional data, and highly class-imbalance databases are the major challenges in the said task. A new method for missing data…

A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function…

This paper presents some considerations about the Goldbach's conjecture (GC). The work is based on elementary results of the number theory and it provides a constructive method that permits, given an even integer, to find at least a pair of…

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis…

Euler's inequality $R\geq 2r$ can be investigated in a novel way by using implicit loci in GeoGebra. Some unavoidable side effects of the implicit locus computation introduce unexpected algebraic curves. By using a mixture of symbolic and…

The highest level of mathematics research is traditionally seen as a solitary activity. Yet new innovations by mathematicians themselves are starting to harness the power of social computation to create new modes of mathematical production.…

Directional data emerges in a wide array of applications, ranging from atmospheric sciences to medical imaging. Modeling such data, however, poses unique challenges by virtue of their being constrained to non-Euclidean spaces like…

A random dot product graph (RDPG) is a generative model for networks in which vertices correspond to positions in a latent Euclidean space and edge probabilities are determined by the dot products of the latent positions. We consider RDPGs…