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.
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.
Probabilistic models often have parameters that can be translated, scaled, permuted, or otherwise transformed without changing the model. These symmetries can lead to strong correlation and multimodality in the posterior distribution over the model's parameters, which can pose challenges both for performing inference a…
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.
New method detects projective equivalences and symmetries in rational 3D curves.
problem Detecting projective equivalences and symmetries in rational 3D curves.
method Using differential invariants and Möbius transformations to avoid solving large polynomial systems.
result Efficient algorithm for detecting projective equivalences and symmetries without solving large polynomial systems.
We introduce an approach based on moving frames for polygon recognition and symmetry detection. We present detailed algorithms for recognition of polygons modulo the special Euclidean, Euclidean, equi-affine, skewed-affine and similarity Lie groups, and explain the procedure for a generic Lie group. The time complexity…
Detecting essential surfaces in 3-manifolds and orbifolds using character varieties.
problem Detecting essential surfaces in 3-manifolds and orbifolds.
method Extending Culler and Shalen's construction to 3-orbifolds using SL2(C) character variety. result Any slope detected on a canonical component of the (P)SL2(C) character variety of a one-cusped hyperbolic 3-manifold with symmetries must be the slope of a symmetric surface. 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 …
In this paper we explore methods to exploit symmetries for ensuring sample efficiency in reinforcement learning (RL), this problem deserves ever increasing attention with the recent advances in the use of deep networks for complex RL tasks which require large amount of training data. We introduce a novel method to dete…
New points detected on surfaces in 4D space, revealing symmetries.
problem Detecting symmetries and special points on surfaces in 4D space.
method Contact classification of symmetric maps from the plane to the plane.
result Special parabolic points detected and associated with sign changes.
Study on metrics on specific nilmanifolds, finding new examples and properties.
problem Characteristically solvable nilmanifolds and their metrics.
method Explicit determination of left-invariant metrics and their properties.
result First known examples of Lie groups without positive index of symmetry.
Least symmetry breaking principle explains SGD's local minima in shallow ReLU networks.
problem Understanding the structure of local minima in two-layer ReLU networks.
method Analyzing the squared loss optimization problem for ReLU networks with Gaussian inputs and applying the principle of least symmetry breaking.
result The principle of least symmetry breaking explains the structure of spurious local minima detected by SGD.
We propose a semantic segmentation model that exploits rotation and reflection symmetries. We demonstrate significant gains in sample efficiency due to increased weight sharing, as well as improvements in robustness to symmetry transformations. The group equivariant CNN framework is extended for segmentation by introdu…
We study control systems invariant under a Lie group with application to the problem of nonlinear trajectory planning. A theory of symmetry reduction of exterior differential systems is employed to demonstrate how symmetry reduction and reconstruction is effective in the explicit, exact construction of planned system t…
GE-autoencoder identifies spontaneous symmetry breaking in systems.
problem Locating phase boundaries and identifying spontaneously broken symmetries in systems.
method Group-equivariant autoencoder using group theory to constrain parameters and learn invariant order parameters.
result GE-autoencoder accurately determines spontaneous symmetry breaking and estimates critical temperatures more efficiently.
The paper explores knotoid invariants on the plane using quandles and cocycles.
problem Classifying planar knotoids due to their complexity and lack of invariants.
method Investigates equivalence of planar knotoids using quandle colorings and cocycle invariants.
result Introduces a new invariant called the triangular quandle cocycle invariant.
GQML uses symmetries from representation theory to improve quantum machine learning.
problem Creating quantum models with symmetries to improve performance.
method Introduction to representation theory for quantum learning, focusing on group actions and symmetries.
result Effective implementation of GQML requires knowledge of group representation theory.
Extends DeTEcT framework for token economies with dynamic and probabilistic parameters.
problem Modeling wealth distribution in token economies with dynamic and probabilistic parameters.
method Introduces four parametrization techniques: dynamic vs static, probabilistic vs non-probabilistic.
result Derives existing wealth distribution models from DeTEcT framework with added restrictions.
A consistent theory of quantum gravity (QG) at Planck scale almost sure contains manifestations of Lorentz local symmetry violations (LV) which may be detected at observable scales. This can be effectively described and classified by models with nonlinear dispersions and related Finsler metrics and fundamental geometri…
Method learns symmetries in curves without augmentation.
problem Symmetries in datasets like rotations and scalings.
method Geometric learning using principal fiber bundles.
result 2-parameter family of canonical curve parameterizations.
New model preserves symmetry in multivariate time series, improving performance.
problem Implicit ordering in MTS models violates inherent exchangeability.
method Permutation-equivariant 2D state space model with canonical architecture.
result Eliminates sequential dependency chains and simplifies stability analysis.
We study the problem of nonparametric dependence detection. Many existing methods may suffer severe power loss due to non-uniform consistency, which we illustrate with a paradox. To avoid such power loss, we approach the nonparametric test of independence through the new framework of binary expansion statistics (BEStat…
Geometric Graph Alignment enhances IoT intrusion detection using NID data.
problem Data scarcity hinders IoT intrusion detection accuracy.
method Geometric Graph Alignment (GGA) approach to transfer knowledge between network intrusion detection and IoT intrusion detection domains.
result GGA approach boosts IoT intrusion detection performance on multiple datasets.
In this letter, we apply the artificial neural network in a supervised manner to map out the quantum phase diagram of disordered topological superconductor in class DIII. Given the disorder that keeps the discrete symmetries of the ensemble as a whole, translational symmetry which is broken in the quasiparticle distrib…
SPTN uses invertible transformations to improve sum-product networks.
problem Improving inference efficiency and tractability in sum-product networks.
method Integrates invertible transformations into sum-product networks (SPNs).
result SPTNs with Gaussian leaves and affine transformations are as tractable as SPNs.
Paper finds new criteria for conjugate points in fluid flows.
problem Finding conjugate points in steady 2D Euler flows.
method Develops a new sufficient criterion for conjugate points, applies to any rotational cell, and uses a general construction of steady fluid surfaces.
result Improves on existing criteria and captures all known conjugate points in rotational cells.
New geometric quantities help classify manifolds and relate to entropy.
problem Classifying Riemannian manifolds using geometric quantities.
method Introducing and analyzing asymptotic geometric quantities like p-capacity, eigenvalues, and Maz'ya constant.
result Geometric quantities coincide with entropy in specific conditions, characterizing manifolds.
LoRAs enable efficient adaptation of large models; this paper explores processing LoRA weights with machine learning.
problem Efficient processing of low-rank weight decompositions in large finetuned models.
method Developed symmetry-aware invariant and equivariant LoL models to process LoRA weights.
result LoL models can predict CLIP scores, finetuning data attributes, and accuracy on downstream tasks.
Study online conformal prediction for non-stationary data with optimal training-conditional regret.
problem Online prediction for non-stationary data streams with unknown distribution drift.
method Proposes split-conformal and full-conformal algorithms that adapt to drift detection and incorporate stability for online learning.
result Proves minimax-optimal regret for online full conformal algorithm under appropriate restrictions.
We propose a new model for digital pathology segmentation, based on the observation that histopathology images are inherently symmetric under rotation and reflection. Utilizing recent findings on rotation equivariant CNNs, the proposed model leverages these symmetries in a principled manner. We present a visual analysi…
In this paper we present a new approach to the study of asymptotically flat static metrics arising in general relativity. In the case where the static potential is bounded, we introduce new quantities which are proven to be monotone along the level set flow of the potential function. We then show how to use these prope…
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.
Paper proves rigidity of static manifolds and applies to metric extensions.
problem Detecting rotational symmetry in static systems.
method Conformal techniques and Minkowski-type inequalities.
result Proves global uniqueness of static metric extensions.
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.
Unified invariant of knots derived from Verma modules.
problem Constructing a unified invariant of knots from quantum sl2.
method Braid groups' action on tensors of Verma modules.
result Unified invariant interpolates colored Jones and ADO polynomials.
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.
Sparse symmetric tensor regression reduces brain connectivity complexity.
problem Complex brain connectivity analysis in neuroimaging.
method Sparse symmetric tensor regression model for functional connectivity.
result Superior performance in Alzheimer's disease detection.
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.
Study of η invariants on lens spaces detects distinctions invisible to ordinary η.
problem Detecting distinctions in η invariants on lens spaces. method Spin-Fourier residues and equivariant η invariants. result Second derivative of the residual η germ is nonzero for some lens spaces. 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…
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.
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.