Sym-NET detects human symmetries in photos, outperforming existing models.
problem Capturing human symmetry perception in real-world images.
method Deep-learning neural network (Sym-NET) trained on MS-COCO dataset with human labels.
result Sym-NET significantly outperforms existing algorithms on unseen MS-COCO photos.
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.
Extends symmetry superalgebras to include all hidden symmetries of manifolds.
problem Tackles hidden symmetries of manifolds generated by Killing spinors.
method Defines generalized symmetry superalgebras, constructs Lie algebra structure, and defines symmetry operators.
result Constructs special Killing-Yano and conformal Killing-Yano forms from bilinears of Killing spinors.
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.
Symmetries of second order ODEs range from 0 to 8, except 7.
problem Understanding the symmetries of second order ODEs.
method Point symmetry analysis of general analytic second order ODEs.
result Symmetry dimension 8 requires local trivializability.
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.
New formulae derived for conformal symmetry breaking operators.
problem Understanding conformal symmetry breaking operators.
method Bernstein-Sato identities for distribution kernels.
result New formulae for conformal symmetry breaking differential operators.
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.
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.
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.
The paper finds formulas for Willmore surfaces and discusses symmetry breaking.
problem Understanding symmetry and symmetry breaking in Willmore surfaces.
method Proved explicit formulas and demonstrated symmetry breaking examples.
result Symmetric boundary conditions do not guarantee symmetric surfaces.
Symmetry in neural networks reduces parameter count without sacrificing accuracy.
problem Improving parameter usage and efficiency in deep neural networks.
method Imposing symmetry constraints on neural network parameters, especially in convolutional and recurrent networks.
result Symmetry can have little or no negative effect on network accuracy, even in deep overparameterized 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.
The paper explores symmetries and conservation laws in Hamiltonian systems.
problem Understanding symmetries and conservation laws in Hamiltonian systems.
method Using dynamical covariant derivative and Jacobi endomorphism, the paper finds invariant equations of symmetries and proves the canonical nonlinear connection can be determined by these symmetries.
result The canonical nonlinear connection can be determined by infinitesimal symmetries and Newtonoid vector fields.
New symmetry found in colored Alexander polynomial.
problem Understanding the structure of colored Alexander polynomials.
method Study of loop and character expansions, group theoretic constraints.
result Existence of a new symmetry in the colored HOMFLY-PT polynomial.
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 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.
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.
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.
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.
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.
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 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.
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.
Exploits symmetries for efficient reinforcement learning with deep networks.
problem Efficient function approximation in reinforcement learning with large data requirements.
method Detects symmetries using reward trails, incorporates them for functional approximation.
result Significant improvement in learning performance by utilizing symmetry information.
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.
The paper studies symmetries in quaternionic geometry and submanifolds.
problem Understanding symmetries in quaternionic geometry and their implications for submanifolds.
method Generalized Feix--Kaledin construction, infinitesimal symmetries analysis, quaternionic and c-projective symmetries study.
result Conditions for extending c-projective symmetries to quaternionic symmetries and studying specific hyperkähler structures.
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 …
Classifies 6-manifolds with maximal symmetry up to diffeomorphism.
problem Classifying 6-manifolds with maximal symmetry.
method Classification based on curvature and symmetry properties.
result Classification of 6-manifolds with almost maximal symmetry rank.
Paper classifies bifurcations of Minkowski symmetry sets for plane curves.
problem Classifying bifurcations of Minkowski symmetry sets.
method Classification of bifurcations based on geometric criteria.
result Different bifurcation types for Minkowski symmetry sets compared to Euclidean symmetry sets.
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.
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.
Study on symmetries of differential equations using gauge transformations and coverings.
problem Understanding the geometry of symmetries in differential equations.
method Interpreting symmetries as gauge transformations and coverings.
result Geometrical insights into λ and μ-symmetries. 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. 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.
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.
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…
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.
Symmetry improves machine learning models by reducing overfitting and complexity.
problem Ignoring symmetry in machine learning models can lead to overfitting and increased complexity.
method Incorporating symmetry into machine learning models, specifically neural networks for classifying handwritten digits.
result Incorporating symmetry into machine learning models reduces overfitting and complexity, requiring less training data and less time to train.
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.