Related papers: Machine Learning Line Bundle Connections

Machine learning is used to approximate the kinetic energy of one dimensional diatomics as a functional of the electron density. The functional can accurately dissociate a diatomic, and can be systematically improved with training. Highly…

In this article we develop a worldline technique based on the method of images to study the effective action associated to Yang-Mills theories on manifolds with boundaries. We consider the possibility of having either relative or absolute…

This article presents differential protection of the distribution line connecting a wind farm in a microgrid. Machine Learning (ML) based models are built using differential features extracted from currents at both ends of the line to…

Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…

We propose a paradigm to deep-learn the ever-expanding databases which have emerged in mathematical physics and particle phenomenology, as diverse as the statistics of string vacua or combinatorial and algebraic geometry. As concrete…

This paper studies binary classification problem associated with a family of loss functions called large-margin unified machines (LUM), which offers a natural bridge between distribution-based likelihood approaches and margin-based…

Understanding the geometry of neural network loss landscapes is a central question in deep learning, with implications for generalization and optimization. A striking phenomenon is linear mode connectivity (LMC), where independently trained…

An active area of investigation in the search for quantum advantage is Quantum Machine Learning. Quantum Machine Learning, and Parameterized Quantum Circuits in a hybrid quantum-classical setup in particular, could bring advancements in…

In this work, we explore advanced machine learning techniques for minimizing Gibbs free energy in full 3D micromagnetic simulations. Building on Brown's bounds for magnetostatic self-energy, we revisit their application in the context of…

Efficient numerical methods to approximate the parallel transport operators of the induced connection on a sub-bundle of a vector bundle are presented. These methods are simpler than naive applications of a Runge--Kutta algorithm, and have…

We relate SLOCC equivalence classes of qudit states to moduli spaces of Calabi-Yau manifolds equipped with a collection of line bundles. The cases of 3 qutrits and 4 qubits are also related to noncommutative algebraic geometry.

Recent research shows that sublevel sets of the loss surfaces of overparameterized networks are connected, exactly or approximately. We describe and compare experimentally a panel of methods used to connect two low-loss points by a low-loss…

Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for a machine learning revolution and have already been profoundly impacted by the…

We review the notions of (weak) Hermitian-Yang-Mills structure and approximate Hermitian-Yang-Mills structure for Higgs bundles. Then, we construct the Donaldson functional for Higgs bundles over compact K\"ahler manifolds and we present…

Determining the optimal model for a given task often requires training multiple models from scratch, which becomes impractical as dataset and model sizes grow. A more efficient alternative is to expand smaller pre-trained models, but this…

In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…

The paper suggest employing machine learning for resource-efficient classification of quantum correlations in entanglement distribution networks. Specifically, artificial neural networks (ANN) are utilized to classify quantum correlations…

This article investigates beam alignment for multi-user millimeter wave (mmWave) massive multi-input multi-output system. Unlike the existing works using machine learning (ML), an alignment method with partial beams using ML (AMPBML) is…

Entanglement is a key quantity for characterizing quantum correlations in particle scattering processes, but its direct evaluation is computationally demanding on quantum hardware. In this work, we investigate whether fermion density…

Recent developments in applied mathematics increasingly employ machine learning (ML)-particularly supervised learning-to accelerate numerical computations, such as solving nonlinear partial differential equations. In this work, we extend…