Related papers: Unsupervised Discovery of Formulas for Mathematica…

The discovery of scientific formulae that parsimoniously explain natural phenomena and align with existing background theory is a key goal in science. Historically, scientists have derived natural laws by manipulating equations based on…

Causal discovery studies the problem of mining causal relationships between variables from data, which is of primary interest in science. During the past decades, significant amount of progresses have been made toward this fundamental data…

Scientific discovery is a complex cognitive process that has driven human knowledge and technological progress for centuries. While artificial intelligence (AI) has made significant advances in automating aspects of scientific reasoning,…

Using a clear and straightforward approach, we discover and prove new binary digit extraction BBP-type formulas for polylogarithm constants. Some known results are also rediscovered in a more direct and elegant manner. Numerous…

Mixtures of factor analysers (MFA) models represent a popular tool for finding structure in data, particularly high-dimensional data. While in most applications the number of clusters, and especially the number of latent factors within…

Artificial intelligence (AI) has been increasingly applied in scientific activities for decades; however, it is still far from an insightful and trustworthy collaborator in the scientific process. Most existing AI methods are either too…

Most convex and nonconvex clustering algorithms come with one crucial parameter: the $k$ in $k$-means. To this day, there is not one generally accepted way to accurately determine this parameter. Popular methods are simple yet theoretically…

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…

In this paper, we propose a constraint-based modeling approach for the problem of discovering frequent gradual patterns in a numerical dataset. This SAT-based declarative approach offers an additional possibility to benefit from the recent…

We propose a new fast fully unsupervised method to discover semantic patterns. Our algorithm is able to hierarchically find visual categories and produce a segmentation mask where previous methods fail. Through the modeling of what is a…

Synthetic data serves as an alternative in training machine learning models, particularly when real-world data is limited or inaccessible. However, ensuring that synthetic data mirrors the complex nuances of real-world data is a challenging…

As artificial intelligence becomes increasingly pervasive and powerful, the ability to audit AI-based systems is growing in importance. However, explainability for artificial intelligence systems is not a one-size-fits-all solution;…

We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…

Pattern discovery algorithms in the music domain aim to find meaningful components in musical compositions. Over the years, although many algorithms have been developed for pattern discovery in music data, it remains a challenging task. To…

Machine learning (ML) and artificial intelligence (AI) algorithms are now being used to automate the discovery of physics principles and governing equations from measurement data alone. However, positing a universal physical law from data…

Determining the number of clusters is a fundamental issue in data clustering. Several algorithms have been proposed, including centroid-based algorithms using the Euclidean distance and model-based algorithms using a mixture of probability…

Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the…

Artificial intelligence (AI) has demonstrated impressive progress in mathematical reasoning, yet its integration into the practice of mathematical research remains limited. In this study, we investigate how the AI Mathematician (AIM) system…

Models with unnormalized probability density functions are ubiquitous in statistics, artificial intelligence and many other fields. However, they face significant challenges in model selection if the normalizing constants are intractable.…

Causal analysis has become an essential component in understanding the underlying causes of phenomena across various fields. Despite its significance, existing literature on causal discovery algorithms is fragmented, with inconsistent…