The paper analyzes symmetries of Vaidya-Bonner geodesics.
problem Investigating invariance properties of Vaidya-Bonner geodesics.
method Classification of Lie point symmetries and Noether symmetries, determination of optimal system of subalgebras.
result Determination of optimal system of subalgebras for Vaidya-Bonner geodesics.
New method detects symmetries beyond affine transformations.
problem Current methods limit symmetry detection to affine transformations.
method Framework for discovering continuous symmetry beyond affine transformations.
result Method is competitive for large sample sizes and superior for small sample sizes.
Humans take advantage of real world symmetries for various tasks, yet capturing their superb symmetry perception mechanism with a computational model remains elusive. Motivated by a new study demonstrating the extremely high inter-person accuracy of human perceived symmetries in the wild, we have constructed the first …
Classifies symmetries of non-flat 3-webs around a point.
problem Understanding symmetries of non-flat 3-webs.
method Classification and construction methods for symmetries.
result Classification of symmetries for non-flat 3-webs.
Geometric mechanism mimics physics' symmetry breaking.
problem Understanding spontaneous symmetry breaking in geometry.
method Analogous to physics, studying symmetry breaking in differential geometry.
result Symmetry breaking can be used to solve geometric problems.
Method improves deep learning models for datasets with mixed approximate symmetries.
problem Improving deep learning models for datasets with mixed approximate symmetries.
method Regularizer-based approach to build models for datasets with mixed approximate symmetries.
result Our method achieves better accuracy than prior approaches while discovering the approximate symmetry levels correctly.
Symmetry in loss functions constrains model parameters, leading to specific learning outcomes.
problem Understanding and leveraging symmetries in neural networks to improve learning outcomes.
method Analyzing the impact of loss function symmetries on model parameters and learning behavior.
result Mirror-reflection symmetries in loss functions lead to constraints on model parameters, influencing learning outcomes.
Approximate symmetries of geodesic equations on 2-spheres are studied. These are the symmetries of the perturbed geodesic equations which represent approximate path of a particle rather than exact path. After giving the exact symmetries of the geodesic equations, two different approaches to study the approximate symmet…
New symmetry dimensions for higher order ODEs are identified.
problem Determining the maximal and submaximal symmetry dimensions for higher order ODEs.
method Cartan-geometric approach to classify symmetry dimensions.
result Next largest realizable symmetry dimensions for scalar ODEs of order ≥ 4 and vector ODEs of order ≥ 3 are determined.
Generalizes symmetries of curved manifolds.
problem Maximizing symmetries in curved manifolds.
method Replaces torus with abelian group, generalizes results.
result Generalizes symmetry results for positively curved manifolds.
Study of continuous symmetries in Nahm data and BPS monopoles.
problem Solutions to Nahm's equations with continuous symmetries.
method Classification of Ansätze and construction of Nahm data.
result Construction of new BPS monopoles with spherical symmetry.
New framework discovers non-affine continuous symmetries in neural networks.
problem Lack of efficient methods for detecting non-affine continuous symmetries in neural networks.
method Computational framework for discovering infinitesimal generators of multi-parameter group actions.
result Framework can discover non-affine continuous symmetries in neural networks.
Researchers discover symmetries in Ricci flows and use them to find invariant solutions.
problem Finding symmetries in Ricci flows on manifolds.
method Developed a method to find Lie point symmetries of Ricci flows and particular metrics.
result Invariant solutions of Ricci flow for specific metric families were obtained.
This paper introduces a new approach to finding knots and links with hidden symmetries using "hidden extensions", a class of hidden symmetries defined here. We exhibit a family of tangle complements in the ball whose boundaries have symmetries with hidden extensions, then we further extend these to hidden symmetries of…
Symmetry in finance is a neglected but potentially valuable concept.
problem The underutilization of symmetry in financial markets.
method Examining symmetry in game theory, technical analysis, and long-term economic growth.
result Symmetry principles can be applied to financial strategies and market dynamics.
Symmetry of neural network densities can be determined from correlation functions.
problem Determining symmetries of neural network densities without knowing the density itself.
method Symmetry-via-duality approach using invariance properties of correlation functions.
result Symmetries of neural network densities can be determined via dual computations of correlation functions.
Symmetries in shrinking Ricci solitons spread outward.
problem Understanding symmetries in shrinking Ricci solitons.
method Propagating approximate symmetries to larger scales.
result Symmetries in shrinking Ricci solitons spread outward.
Clarifies relation between Pfaffian fibrations and relative algebroids.
problem Understanding geometric structures and symmetries in PDEs.
method Introduces and analyzes Pfaffian fibrations and relative algebroids, clarifying their relationship.
result Every Pfaffian fibration induces a relative algebroid, and their prolongations and local solutions coincide.
Classifies Lie symmetry algebras for 2D quasilinear equations, linking symmetry to linearity.
problem Classifying Lie symmetry algebras for 2D quasilinear equations.
method Classification based on abelian Lie symmetry algebras of dimension and rank.
result Equations with specific symmetry algebras are linearizable.
This work relaxes GNN symmetries to approximate automorphisms, improving model performance.
problem Improving graph neural network performance on asymmetric graphs.
method Formalizing approximate symmetries via graph coarsening, introducing a bias-variance formula.
result Best generalization performance achieved by choosing a larger symmetry group than automorphisms but smaller than permutations.
Noether's theorem clarifies how symmetries in neural networks influence learning.
problem Understanding how symmetries in neural networks affect learning.
method Systematic study of symmetry interactions with learning algorithms using Noether's theorem.
result Symmetries impose restrictions on the optimization path, leading to conserved quantities.
Researchers create BPS monopoles with any desired symmetry breaking.
problem Creating monopoles with specific symmetry breaking patterns.
method Using a new class of Nahm data to construct finite energy BPS monopoles.
result Arbitrary symmetry breaking monopoles can be constructed.
This paper aims to incorporate passive symmetries in machine learning for better generalization.
problem Machine learning's reliance on arbitrary choices leads to passive symmetries that can limit generalization.
method Translation among physics, mathematics, and machine learning to understand and implement passive symmetries.
result Respecting passive symmetries can improve machine learning's ability to generalize.
SymPE breaks symmetries in equivariant networks, improving performance across various tasks.
problem Equivariant networks cannot break symmetries, leading to poor performance in tasks with symmetrical inputs.
method Novel equivariant conditional distributions and randomized canonicalization.
result SymPE significantly improves performance of group-equivariant and graph neural networks.
Study of symmetries in 2D Yang-Mills theory, including orbifolds and higher forms.
problem Understanding symmetries and anomalies in 2D Yang-Mills theory.
method Combining continuum methods, topological defects, and higher gauge theory.
result Unified description of higher and lower form gauge fields, identifying spontaneous symmetry breaking.
We exploit the symmetry concepts developed in the companion review of this article to introduce a stochastic version of link reversal symmetry, which leads to an improved understanding of the reciprocity of directed networks. We apply our formalism to the international trade network and show that a strong embedding in …
The study examines symmetries in spaces with positive or non-negative curvature.
problem Understanding symmetries in spaces with curvature constraints.
method Survey of existing results for Riemannian manifolds with specified curvature properties and symmetries.
result Results on symmetries in spaces with curvature bounds.
Symmetries of Einstein-Weyl manifolds can be extended from boundary surfaces.
problem Extending symmetries from boundary surfaces to Einstein-Weyl manifolds.
method Starting from a symmetry of conformal Cartan connection on a boundary surface, proving symmetries can be extended.
result Symmetries of conformal Cartan connection on the boundary can be extended to symmetries of the Einstein-Weyl manifold.
We propose to impose symmetry in neural network parameters to improve parameter usage and make use of dedicated convolution and matrix multiplication routines. Due to significant reduction in the number of parameters as a result of the symmetry constraints, one would expect a dramatic drop in accuracy. Surprisingly, we…
We classify hyperbolic monopoles with continuous symmetries and construct new examples.
problem Classifying and constructing hyperbolic monopoles with continuous symmetries.
method Developed a Structure Theorem and used representation theory to simplify the problem.
result Found constraints on structure groups and constructed novel spherically symmetric Sp(n) hyperbolic monopoles. Symmetry-breaking in three differential geometry conjectures.
problem Exploring the role of symmetry in three differential geometry conjectures.
method Examining the Carathéodory, Willmore, and Lawson Conjectures through the lens of symmetry in 3D space-forms.
result Symmetry is broken, and more general ambient metrics are considered, leading to the failure of the conjectures.
Metric evaluates symmetry-breaking in datasets, revealing severe biases.
problem Symmetry-breaking in datasets can hinder the performance of symmetry-aware methods.
method Developed a metric to quantify symmetry-breaking using a two-sample classifier test.
result Symmetry-breaking can prevent optimal performance of invariant methods, even when labels are invariant.
Lie symmetry group method is applied to study the Born-Infeld equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra symmetries is determined.
A condition for a statistical manifold to have an equiaffine structure is studied. The facts that dual flatness and conjugate symmetry of a statistical manifold are sufficient conditions for a statistical manifold to have an equiaffine structure were obtained in [2] and [3]. In this paper, a fact that a statistical man…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of geometric symmetry of a linearly singular differential equation is introduced as a trans…
Researchers develop Orlov-Schulman symmetries for self-dual conformal structures.
problem Developing symmetries for self-dual conformal structures.
method Explicit proof of compatibility with Lax-Sato flows, dressing scheme based on Riemann-Hilbert problem.
result Construction and proof of compatibility of Orlov-Schulman symmetries.
A reduction method of ODEs not possessing Lie point symmetries makes use of the so called λ-symmetries (C. Muriel and J. L. Romero, \emph{IMA J. Appl. Math.} \textbf{66}, 111-125, 2001). The notion of covering for an ODE Y is used here to recover λ-symmetries of Y as nonlocal symmetries. In …
New triangulations of quaternionic projective plane found with various symmetry groups.
problem Classifying triangulations of quaternionic projective plane with 15 vertices.
method Constructing and classifying 15-vertex triangulations with various symmetry groups.
result Exactly 75 triangulations of quaternionic projective plane with 15 vertices and symmetry group of order at least 4.
New tools compute index of symmetry in homogeneous fibrations.
problem Computing the index of symmetry in homogeneous fibrations.
method Developed new tools to compute the index of symmetry.
result Determined the index of symmetry of various homogeneous spaces.
This paper classifies topological symmetry groups for Petersen family graphs.
problem Understanding symmetries of graphs embedded in 3D space.
method Examined all embeddings of Petersen family graphs in S3 and classified their topological symmetry groups. result Identified all possible groups that can be realized as topological symmetry groups for each graph in the Petersen family.
We generalize the symmetry superalgebras of isometries and geometric Killing spinors on a manifold to include all the hidden symmetries of the manifold generated by Killing spinors in all dimensions. We show that bilinears of geometric Killing spinors produce special Killing-Yano and special conformal Killing-Yano form…
We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetries can be seen as solutions of a hierarchy of linear differential systems. We show that the existence of rational symmetries constrains the …
The paper explores variational principles for equations of maximal symmetry, providing new insights and results.
problem Exploring variational principles for equations of maximal symmetry.
method Study of variational and divergence symmetries for linear and nonlinear equations of maximal symmetry, providing first integrals in explicit form.
result Significantly different results and more general variational symmetry algebra for linear and nonlinear equations compared to previous studies.
Bayesian framework detects symmetries in chaotic dynamical systems.
problem Detecting symmetries in chaotic attractors for insights into dynamical system structure.
method Bayesian framework using Gibbs posterior constructed from Wasserstein distances.
result Bayesian framework accurately recovers symmetries under high noise and small sample sizes.
The paper characterizes strong Hamel functions using symmetries and proves their preservation properties.
problem Characterizing strong Hamel functions and their symmetries in Finsler spaces.
method Analyzing geodesic spray, strong dual symmetries, and strong dynamical symmetries.
result Strong Hamel functions can be characterized in terms of strong dual symmetries and strong dynamical symmetries.
Study on geodesics in a specific sub-Riemannian structure with two types of behavior.
problem Symmetries and geodesics in a sub-Riemannian structure with growth vector (4,7).
method Symmetry reduction to analyze geodesics.
result Existence of two distinct types of geodesics: those that avoid the fixed point set and those that are contained within it.
In this paper we study the infinitesimal symmetries, Newtonoid vector fields, infinitesimal Noether symmetries and conservation laws of Hamiltonian systems. Using the dynamical covariant derivative and Jacobi endomorphism on the cotangent bundle we find the invariant equations of infinitesimal symmetries and Newtonoid …
New findings on hidden symmetries in ReLU networks.
problem Understanding the redundancy and symmetries in ReLU network parameter space.
method Analyzing parameter settings and function classes for various network architectures.
result For certain network architectures, there are no hidden symmetries.