相关论文: Machine Learning Class Numbers of Real Quadratic F…

Machine learning models can make critical errors that are easily hidden within vast amounts of data. Such errors often run counter to rules based on human intuition. However, rules based on human knowledge are challenging to scale or to…

This article conducts a large dimensional study of a simple yet quite versatile classification model, encompassing at once multi-task and semi-supervised learning, and taking into account uncertain labeling. Using tools from random matrix…

We present a novel hierarchical approach to multi-class classification which is generic in that it can be applied to different classification models (e.g., support vector machines, perceptrons), and makes no explicit assumptions about the…

We classify all quadratic imaginary number fields that have a Euclidean ideal class. There are seven of them, they are of class number at most two, and in each case the unique class that generates the class-group is moreover norm-Euclidean.

There is a growing need for investigating how machine learning models operate. With this work, we aim to understand trained machine learning models by questioning their data preferences. We propose a mathematical framework that allows us to…

Predicting the outcome of liquid droplet collisions is an extensively studied phenomenon but the current physics based models for predicting the outcomes are poor (accuracy $\approx 43\%$). The key weakness of these models is their limited…

In this paper, we calculate the unit groups and the $2$-class numbers of the fields $ \mathbb{K}= \mathbb{Q}(\sqrt{2}, \sqrt{p_1}, \sqrt{p_2})$ and $ \mathbb{L}= \mathbb{Q}( \sqrt{-1},\sqrt{2}, \sqrt{p_1}, \sqrt{p_2})$, where $p_1$ and…

Although learning in high dimensions is commonly believed to suffer from the curse of dimensionality, modern machine learning methods often exhibit an astonishing power to tackle a wide range of challenging real-world learning problems…

Recent times are witnessing rapid development in machine learning algorithm systems, especially in reinforcement learning, natural language processing, computer and robot vision, image processing, speech, and emotional processing and…

Quantum machine learning, as an extension of classical machine learning that harnesses quantum mechanics, facilitates effiient learning from data encoded in quantum states. Training a quantum neural network typically demands a substantial…

Learning Spaces are certain set systems that are applied in the mathematical modeling of education. We propose a suitable compression (without loss of information) of such set systems to facilitate their logical and statistical analysis.…

Uncertainty in machine learning models is a timely and vast field of research. In supervised learning, uncertainty can already occur in the first stage of the training process, the annotation phase. This scenario is particularly evident…

High-multiplicity signatures at particle colliders can arise in Standard Model processes and beyond. With such signatures, difficulties often arise from the large dimensionality of the kinematic space. For final states containing a single…

Using numerical data coming from Monte Carlo simulations of four-dimensional Causal Dynamical Triangulations, we study how automated machine learning algorithms can be used to recognize transitions between different phases of quantum…

In conventional supervised learning, a training dataset is given with ground-truth labels from a known label set, and the learned model will classify unseen instances to known labels. This paper studies a new problem setting in which there…

The capabilities of supervised machine learning (SML), especially compared to human abilities, are being discussed in scientific research and in the usage of SML. This study provides an answer to how learning performance differs between…

A way to construct and classify the three dimensional polynomially deformed algebras is given and the irreducible representations is presented. for the quadratic algebras 4 different algebras are obtained and for cubic algebras 12 different…

The standard approach to contrastive learning is to maximize the agreement between different views of the data. The views are ordered in pairs, such that they are either positive, encoding different views of the same object, or negative,…

Issues concerning intelligent data analysis occurring in machine learning are investigated. A scheme for synthesizing correct supervised classification procedures is proposed. These procedures are focused on specifying partial order…

The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in…