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…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
Trend · papers per month
48 results for “Hidden symmetries”
Study shows most hyperbolic knot complements lack hidden symmetries.
problem Proving most knot complements lack hidden symmetries.
method Using rational functions on varieties associated to a link.
result Most knot complements lack hidden symmetries.
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.
The paper proves limitations on hyperbolic knot complements with hidden symmetries.
problem Identifying hyperbolic knot complements with hidden symmetries.
method Obstructions to infinitely many fillings producing knot complements with hidden symmetries.
result The figure-eight knot complement is the only hyperbolic knot complement with hidden symmetries.
The paper studies symmetries and hidden symmetries of twisted knot complements.
problem Analyzing symmetries and hidden symmetries of -twisted knot complements.
method Analysis via long Dehn fillings on fully augmented links complements.
result No hidden symmetries in -twisted knot complements, implying at most two commensurability classes.
We briefly review the hierarchy for the hyper-Kähler equations and define a notion of symmetry for solutions of this hierarchy. A four-dimensional hyper-Kähler metric admits a hidden symmetry if it embeds into a hierarchy with a symmetry. It is shown that a hyper-Kähler metric admits a hidden symmetry if it admits a ce…
The paper studies arithmeticity and hidden symmetries in fully augmented pretzel link complements.
problem Determining arithmeticity and commensurability of fully augmented pretzel link complements.
method Careful analysis of geometry, including cusp shapes and totally geodesic surfaces.
result Construction of two infinite families of non-arithmetic fully augmented link complements.
A "hidden symmetry" of a Riemannian manifold M is an isometry of a d-sheeted, 1<d<\infty, Riemannian cover of M which is not the lift of any isometry. In this paper we characterize the locally symmetric metric(s) on a closed, arithmetic manifold as the unique metric with infinitely many hidden symmetries.
Some natural hidden symmetries in the Verma modules over the Virasoro algebra are constructed in terms of geometric quantization. Their differential geometric meaning is established and their expression via -conformal symmetries in the Verma modules over the Lie algebra is found. The analysis and the unr…
This paper provides two obstructions to small knot complements in admitting hidden symmetries. The first obstruction is being cyclically commensurable with another knot complement. This result provides a partial answer to a conjecture of Boileau, Boyer, Cebanu, and Walsh. We also provide a second obstruction to a…
Study on hidden symmetries in Dehn fillings of tetrahedral links.
problem Existence of infinite families of knot complements with hidden symmetries.
method Analysis of horoball packings and SnapPy algorithm.
result No infinite families of knot complements with hidden symmetries exist for given tetrahedral links and related manifolds.
Minimal model reveals how permutation symmetry affects unsupervised learning.
problem Understanding permutation symmetry in unsupervised learning.
method Proposed a minimal model with two hidden units in a restricted Boltzmann machine.
result Proved that critical data size is independent of the number of hidden units once finite.
Study symmetric linear bandits with hidden symmetry, achieving improved regret bounds.
problem High-dimensional linear bandits with hidden symmetry.
method Model selection within low-dimensional subspaces to learn hidden symmetry.
result Achieved improved regret bounds of and .
Hidden symmetries and the generic spectral setting of generalized laplacians on homogeneous spacesmath.DG
Study spectral settings of generalized Laplacians on homogeneous spaces.
problem Understanding the spectral properties of generalized Laplacians on compact homogeneous spaces.
method Investigates the generic spectral configuration of operators on -invariant metrics on .
result The spectral setting depends on -isometries and hidden symmetries.
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…
Effective action for Kerr-Newman black hole found in twistor theory.
problem Effective action for Kerr-Newman black hole.
method Twistor particle theory to achieve all-orders worldline effective action.
result Exact hidden symmetries identified in self-dual backgrounds.
Study generalizes Yang-Mills equations for special complex surfaces.
problem Deriving equations for self-dual Yang-Mills fields on complex surfaces.
method Generalization of flat space Yang's and Newman's equations to conformally Kahler Riemannian 4-manifolds.
result Continuous group of hidden symmetries found only for conformally half-flat geometry.
In this article we examine the conjecture of Neumann and Reid that the only hyperbolic knots in the -sphere which admit hidden symmetries are the figure-eight knot and the two dodecahedral knots. Knots whose complements cover hyperbolic reflection orbifolds admit hidden symmetries, and we verify the Neumann-Reid con…
The paper explores hidden torus symmetries in integrable systems and their stability.
problem Structural stability of singularities in integrable systems.
method Use of hidden torus actions near singular orbits and integrable perturbations.
result Persistence of toric symmetries and structural stability of Kalashnikov's parabolic orbits.
The moduli space of the Calabi-Yau three-folds, which play a role as superstring ground states, exhibits the same {\em special geometry} that is known from nonlinear sigma models in supergravity theories. We discuss the symmetry structure of special real, complex and quaternionic spaces. Maps between these spaces…
Hidden symmetry of a G'-space X is defined by an extension of the G'-action on X to that of a group G containing G' as a subgroup. In this setting, we study the relationship between the three objects: (A) global analysis on X by using representations of G (hidden symmetry); (B) global analysis on X by using representat…
Mixed-platonic 3-manifoldsmath.GT
New mixed-platonic 3-manifolds from different polyhedra types.
problem Finding new hyperbolic knot complements with hidden symmetries.
method Defined mixed-platonic 3-manifolds and studied their properties.
result No mixed-platonic hyperbolic knot complement has hidden symmetries.
Symmetry-regularized Neural ODEs improve model stability and interpretability.
problem Improving the stability and physical interpretability of Neural ODEs.
method Integrating Lie symmetries and conservation laws into the loss function.
result Symmetry-regularized Neural ODEs enhance model stability and interpretability.
The relations between the infinite dimensional geometry of -conformal symmetries at , Berezin quantization of the Lobachevskii plane and Karasev-Maslov asymptotic quantization are explicated. Some aspects of the ``approximate'' representation theory are discussed.
Study finds necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.
problem Understanding the asymptotic behavior of black hole geometries.
method Used hidden symmetry and conformal geometry technology to find necessary conditions.
result Necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.
Hyperbolic knots decompose into prism orbifolds.
problem Understanding hyperbolic knot complements and their geometric properties.
method Analyzing knot complements as quotients of by discrete groups of reflections in polyhedra with triangular prism combinatorial type.
result Knot complements decompose into hidden symmetries and contain closed, embedded, totally geodesic surfaces.
Rolling balls and Octonionsmath.OC
In this semi-expository paper we disclose hidden symmetries of a classical nonholonomic kinematic model and try to explain geometric meaning of basic invariants of vector distributions.
Quantum Fourier Transform aids machine learning inference.
problem Generalizing from finite data samples to ground truth.
method Inspired by quantum algorithms, uses Quantum Fourier Transform to expose invariant subspace for data comparison.
result Proposes a concrete implementation for machine learning applications leveraging symmetries.
In this paper, we show that any non-arithmetic hyperbolic -bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic -bridge link complement cannot irregularly cover a hyperbolic -manifold. By combining this corollary with the work of Boileau and Weidmann, we obtain a ch…
Coexisting Hidden and self-excited attractors in an economic system of integer or fractional orderq-fin.GN
Paper analyzes coexisting hidden and self-excited attractors in an economic system.
problem Existence of coexisting hidden and self-excited attractors in economic systems.
method Integer and fractional order analysis of an economic system.
result Integer-order system exhibits multiple combinations of coexisting hidden and self-excited attractors.
Hidden symmetries of the Goryachev-Chaplygin and Kovalevskaya gyrostats spacetimes, as well as the Brdička-Eardley-Nappi-Witten pp-waves are studied. We find out that these spacetimes possess higher rank Stäckel-Killing tensors and that in the case of the pp-wave spacetimes the symmetry group of the Stäckel-Killing ten…
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.
Study shows no hidden symmetries in specific spacetime metrics.
problem Demonstrating the absence of Killing tensors in Koutras-McIntosh spacetimes.
method Geometric theory of overdetermined PDEs and Cartan prolongation-projection method.
result No Killing tensors of low degrees in Wils metrics and generic pp-waves.
We consider four (real or complex) dimensional hyper-Kähler metrics with a conformal symmetry K. The three-dimensional space of orbits of K is shown to have an Einstein-Weyl structure which admits a shear-free geodesics congruence for which the twist is a constant multiple of the divergence. In this case the Einstein-W…
New insights into hidden minima in neural networks.
problem Identifying hidden minima in two-layer ReLU networks.
method Analyzing curves along which loss is minimized, focusing on eigenvalue contributions.
result Distinctive structural and symmetry properties of arcs emanating from hidden minima.
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 learning curves in simplified situations. The performance for learning drifting concep…
Symmetric functions learn better with strategic initial conditions.
problem Understanding how to improve learning efficiency for symmetric functions in neural networks.
method Investigates the impact of initial conditions on SGD training for symmetric functions in neural networks with one hidden layer.
result Strategic initial conditions can lead to efficient generalization guarantees for learning symmetric functions.
We describe a quaternionic-based Ansatz generalizing the Gibbons-Hawking Ansatz to a class of hyperkähler metrics with hidden symmetries. We then apply it to obtain explicit expressions for gravitational instanton metrics of type .
Locally Homogeneous Spaces, Induced Killing Vector Fields and Applications to Bianchi Prototypesmath.DG
An answer to the question: Can, in general, the adoption of a given symmetry induce a further symmetry, which might be hidden at a first level? has been attempted in the context of differential geometry of locally homogeneous spaces. Based on E. Cartan's theory of moving frames, a methodology for finding all symmetries…
Equivariant cohomology simplifies symplectic manifold integrals with group actions.
problem Complex integrals on symplectic manifolds with Lie group actions.
method Atiyah-Bott Localization Theorem
result Simplifies integrals by revealing hidden structure.
Study reveals different types of critical points in shallow neural networks.
problem Optimization challenges in two-layer ReLU networks with symmetry.
method Symmetry analysis, bifurcation theory, and geometric group actions.
result Different types of spurious minima have distinct loss behavior.
Akbulut has recently shown that an infinite family of Cappell-Shaneson homotopy 4-spheres is diffeomorphic to the standard 4-sphere. In the present paper, a strictly larger family is shown to be standard by a simpler method. This new approach uses no Kirby calculus except through the relatively simple 1979 paper of Akb…
Deep networks exhibit permutation saddles and valleys between equivalent minima.
problem Understanding the structure of loss landscapes in deep neural networks.
method Geometric approach to constructing paths between equivalent minima and saddle points.
result Existence of permutation saddles and valleys in deep neural networks.
Study shows arithmetic properties of specific hyperbolic Dehn fillings.
problem Arithmeticity of one-cusped Dehn fillings of specific link complements.
method Investigation of cusp fields, trace fields, and invariant trace fields.
result No one-cusped hyperbolic Dehn filling of the Berge manifold is arithmetic.
This paper opens the series of articles supplemental to the series (hep-th/9405050,q-alg/9610026,q-alg/9611003,q-alg/9611019,funct-an/9611003), which also lies in lines of general ideology exposed in the review (mp_arc/96-477). The main purpose of the activity, which has its origin and motivation presumably in the auth…
We consider a binary sequence generated by thresholding a hidden continuous sequence. The hidden variables are assumed to have a compound symmetry covariance structure with a single parameter characterizing the common correlation. We study the parameter estimation problem under such one-parameter models. We demonstrate…
Analyzes the Hessian of ReLU networks, proving skewed eigenvalue distribution.
problem Characterizing the Hessian at spurious minima in shallow ReLU models.
method Symmetry breaking and representation theory techniques.
result Proves skewed eigenvalue distribution of Hessian at spurious minima.
Study shows directional convergence for neural networks under spherical symmetry.
problem Learning linear predictors with neural networks under spherically symmetric data.
method Analysis of gradient flow and gradient descent for two-layer and deep linear networks.
result Directional convergence guarantees with exact convergence rate for specific network architectures.