Related papers: Machine-learning hidden symmetries
Recently, a remarkable new class of spacetimes describing black holes immersed in a non-aligned electromagnetic field has been found. While still of type D, this class goes beyond the famous Pleba\'nski--Demia\'nski family. Here we…
Most distinguishing features of black holes and their mimickers are concentrated near the horizon. In contrast, astrophysical observations and theoretical considerations primarily constrain the far-field geometry. In this work we develop…
Hybrid methods have been shown to outperform pure statistical and pure deep learning methods at both forecasting tasks, and at quantifying the uncertainty associated with those forecasts (prediction intervals). One example is Multivariate…
Different astrophysical methods can be combined to detect possible deviations from General Relativity. In this work, we consider a class of $f(R)$ gravity models selected by the existence of Noether symmetries. In this framework, it is…
We demonstrate that the rotating black holes in an arbitrary number of dimensions and without any restrictions on their rotation parameters possess the same `hidden' symmetry as the 4-dimensional Kerr metric. Namely, besides the spacetime…
We describe some classes of PDE that display hidden symmetry, with reduced equations having additional symmetry operators compared to the initial equations. Relations between the concepts of hidden and conditional symmetry, and between…
Nonlinear supersymmetry is characterized by supercharges to be higher order in bosonic momenta of a system, and thus has a nature of a hidden symmetry. We review some aspects of nonlinear supersymmetry and related to it exotic supersymmetry…
In numerical modeling of the Earth System, many processes remain unknown or ill represented (let us quote sub-grid processes, the dependence to unknown latent variables or the non-inclusion of complex dynamics in numerical models) but…
A key element of any machine learning algorithm is the use of a function that measures the dis/similarity between data points. Given a task, such a function can be optimized with a metric learning algorithm. Although this research field has…
In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive…
Deep learning approaches to anomaly detection have recently improved the state of the art in detection performance on complex datasets such as large collections of images or text. These results have sparked a renewed interest in the anomaly…
The Hidden Markov Model (HMM) is one of the most widely used statistical models for sequential data analysis. One of the key reasons for this versatility is the ability of HMM to deal with missing data. However, standard HMM learning…
We discuss probabilistic neural networks with a fixed internal representation as models for machine understanding. Here understanding is intended as mapping data to an already existing representation which encodes an {\em a priori}…
When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of…
We propose Fiber Bundle Networks (FiberNet), a novel machine learning framework integrating differential geometry with machine learning. Unlike traditional deep neural networks relying on black-box function fitting, we reformulate…
We present and analyse three online algorithms for learning in discrete Hidden Markov Models (HMMs) and compare them with the Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalisation error we draw…
Hamiltonian Learning is a process of recovering system Hamiltonian from measurements, which is a fundamental problem in quantum information processing. In this study, we investigate the problem of learning the symmetric Hamiltonian from its…
Motivated by recent progresses in the holographic descriptions of the Kerr and Reissner-Nordstr{\o}m (RN) black holes, we explore the hidden conformal symmetry of nonextremal uplifted 5D RN black hole by studying the near horizon wave…
Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…
We analyze the performance of a class of manifold-learning algorithms that find their output by minimizing a quadratic form under some normalization constraints. This class consists of Locally Linear Embedding (LLE), Laplacian Eigenmap,…