Related papers: Mathematical conjecture generation using machine i…

Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances…

Clustering has become a core technology in machine learning, largely due to its application in the field of unsupervised learning, clustering, classification, and density estimation. A frequentist approach exists to hand clustering based on…

The increasing realism of generated images has raised significant concerns about their potential misuse, necessitating robust detection methods. Current approaches mainly rely on training binary classifiers, which depend heavily on the…

During the past two decades there has been a lot of interest in developing statistical depth notions that generalize the univariate concept of ranking to multivariate data. The notion of depth has also been extended to regression models and…

We propose a simple yet effective solution to tackle the often-competing goals of fairness and utility in classification tasks. While fairness ensures that the model's predictions are unbiased and do not discriminate against any particular…

Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…

In this work we: (1) review likelihood-based inference for parameter estimation and the construction of confidence regions; and, (2) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar…

3D generative modeling is accelerating as the technology allowing the capture of geometric data is developing. However, the acquired data is often inconsistent, resulting in unregistered meshes or point clouds. Many generative learning…

Machine learning (ML) may be oblivious to human bias but it is not immune to its perpetuation. Marginalisation and iniquitous group representation are often traceable in the very data used for training, and may be reflected or even enhanced…

The aim of this review is to present and analyze the probabilistic models of mathematical phylogenetics which have been intensively used in recent years in biology as the cornerstone of attempts to infer and reconstruct the ancestral…

Closed-form, interpretable mathematical models have been instrumental for advancing our understanding of the world; with the data revolution, we may now be in a position to uncover new such models for many systems from physics to the social…

In this work we employ machine learning to understand structured mathematical data involving finite groups and derive a theorem about necessary properties of generators of finite simple groups. We create a database of all 2-generated…

Generative models have enjoyed widespread success in a variety of applications. However, they encounter inherent mathematical limitations in modeling distributions where samples are constrained by equalities, as is frequently the setting in…

Artificial intelligence is beginning to reduce the manual effort in the CAD-to-mesh pipeline. Written for meshing and geometry practitioners with limited AI background, this survey organizes recent work by workflow step. We cover part…

We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…

The vast corpus of physics equations forms an implicit network of mathematical relationships that traditional analysis cannot fully explore. This work introduces a graph-based framework combining neural networks with symbolic analysis to…

Fairness in machine learning is increasingly critical, yet standard approaches often treat data as static points in a high-dimensional space, ignoring the underlying generative structure. We posit that sensitive attributes (e.g., race,…

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…

This paper presents two concrete applications of Artificial Intelligence to algorithmic and analytic number theory. Recent benchmarks of large language models have mainly focused on general mathematics problems and the currently infeasible…

Bayesian Generative AI (BayesGen-AI) methods are developed and applied to Bayesian computation. BayesGen-AI reconstructs the posterior distribution by directly modeling the parameter of interest as a mapping (a.k.a. deep learner) from a…