Related papers: Machine Learning Mutation-Acyclicity of Quivers

Machine learning is becoming an increasingly valuable tool in mathematics, enabling one to identify subtle patterns across collections of examples so vast that they would be impossible for a single researcher to feasibly review and analyze.…

Cluster algebras have recently become an important player in mathematics and physics. In this work, we investigate them through the lens of modern data science, specifically with techniques from network science and machine learning. Network…

Machine Learning (ML) serves as a general-purpose, highly adaptable, and versatile framework for investigating complex systems across domains. However, the resulting computational resource demands, in terms of the number of parameters and…

Quantum machine learning (QML) is a promising early use case for quantum computing. There has been progress in the last five years from theoretical studies and numerical simulations to proof of concepts. Use cases demonstrated on…

We use machine learning to classify examples of braids (or flat braids) as trivial or non-trivial. Our ML takes form of supervised learning using neural networks (multilayer perceptrons). When they achieve good results in classification, we…

Quantum Machine Learning (QML) models are aimed at learning from data encoded in quantum states. Recently, it has been shown that models with little to no inductive biases (i.e., with no assumptions about the problem embedded in the model)…

Machine learning (ML) methods such as artificial neural networks are rapidly becoming ubiquitous in modern science, technology and industry. Despite their accuracy and sophistication, neural networks can be easily fooled by carefully…

Quantum Machine Learning (QML) shows how it maintains certain significant advantages over machine learning methods. It now shows that hybrid quantum methods have great scope for deployment and optimisation, and hold promise for future…

The primary aim of this paper is to comprehend, assess, and analyze the role, relevance, and efficiency of machine learning models in predicting heart disease risks using clinical data. While the importance of heart disease risk prediction…

Distance metric learning aims to learn from the given training data a valid distance metric, with which the similarity between data samples can be more effectively evaluated for classification. Metric learning is often formulated as a…

Quantum Machine Learning (QML) is an exciting tool that has received significant recent attention due in part to advances in quantum computing hardware. While there is currently no formal guarantee that QML is superior to classical ML for…

In this work, we perform a comprehensive study of the machine learning (ML) methods for the purpose of characterising the quantum set of correlations. As our main focus is on assessing the usefulness and effectiveness of the ML approach, we…

Machine learning, a branch of artificial intelligence, learns from previous experience to optimize performance, which is ubiquitous in various fields such as computer sciences, financial analysis, robotics, and bioinformatics. A challenge…

In recent years, supervised and semi-supervised machine learning methods such as neural networks, support vector machines (SVM), and semi-supervised support vector machines (S4VM) have been widely used in quantum entanglement and quantum…

Quiver mutation plays a crucial role in the definition of cluster algebras by Fomin and Zelevinsky. It induces an equivalence relation on the set of all quivers without loops and two-cycles. A quiver is called mutation-acyclic if it is…

Quantum machine learning (QML) has witnessed immense progress recently, with quantum support vector machines (QSVMs) emerging as a promising model. This paper focuses on the two existing QSVM methods: quantum kernel SVM (QK-SVM) and quantum…

Totally proper quivers, introduced by S.~Fomin and the author arXiv:2406.03604, have many useful properties including powerful mutation invariants. We show that every mutation-acyclic quiver (i.e., a quiver that is mutation equivalent to an…

Machine-learning (ML) ans\"atze have greatly expanded the accuracy and reach of variational quantum Monte Carlo (QMC) calculations, in particular when exploring the manifold quantum phenomena exhibited by spin systems. However, the…

Acyclic cluster algebras have an interpretation in terms of tilting objects in a Calabi-Yau category defined by some hereditary algebra. For a given quiver $Q$ it is thus desirable to decide if the cluster algebra defined by $Q$ is acyclic.…

We present a geometric realization for all mutation classes of quivers of rank $3$ with real weights. This realization is via linear reflection groups for acyclic mutation classes and via groups generated by $\pi$-rotations for the cyclic…