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…
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48 results for “approximate symmetries”
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.
New method approximates curvature from symmetries in deep networks.
problem Hard to approximate curvature in large deep networks.
method Analytically averaging over group actions that leave the loss invariant to construct structured Hessian approximations.
result Structured Hessian approximations from single gradients can be estimated, stored, and inverted.
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.
The paper investigates how symmetry in models affects their performance and generalization.
problem Understanding how symmetry in models impacts their performance and generalization.
method Formal unified investigation of intuitions about symmetry in models and data.
result Quantitative bounds and comparisons between model and data equivariance lead to optimal model performance.
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 method uses scalar-based models to approximate spherical tensors efficiently.
problem Efficiently approximating spherical tensors with equivariant functions.
method Expressing equivariant functions as the product of a scalar function and a small tensor basis.
result Approximations are fast, simple to implement, and accurate in practical settings.
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.
Unified method for CNNs to approximate equivariant maps across various groups.
problem Limited universal approximation theorems for CNNs with specific groups and settings.
method Unified approach to derive universal approximation theorems for equivariant maps by CNNs in diverse settings.
result Ability to handle non-linear equivariant maps between infinite-dimensional spaces for non-compact groups.
Generalized Guarantees for Variational Inference in the Presence of Even and Elliptical Symmetrystat.ML
New guarantees for VI in symmetric cases, extending previous results.
problem Symmetry in variational inference for complex distributions.
method Analysis of -divergences and their stationary points under symmetry.
result Symmetry-matching principles ensure recovery of mean and correlation matrix.
New framework uses symmetry-based matrices for efficient, flexible NNs.
problem Designing neural networks with relaxed equivariance.
method Symmetry-based structured matrices, Group Matrices (GMs).
result GMs enable competitive performance with fewer parameters.
Develops approximately equivariant neural processes for better data modeling.
problem Real-world data often breaks exact equivariance; how to model this?
method General approach to creating approximately equivariant architectures, applicable to any model and symmetry group.
result Approximately equivariant neural processes outperform non-equivariant and strictly equivariant models in regression tasks.
BEAUTY Powered BEASTstat.ME
A new test method improves goodness-of-fit tests for copulas.
problem Developing robust tests for copula goodness-of-fit.
method Binary Expansion Approximation of UniformiTY (BEAUTY) and Binary Expansion Adaptive Symmetry Test (BEAST).
result The BEAST method improves empirical power against various alternatives.
Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaceshep-th
The paper finds compact symbolic approximations for Ricci-flat metrics using Calabi-Yau hypersurfaces.
problem Finding explicit constructions of Ricci-flat metrics on Calabi-Yau manifolds remains challenging.
method Analysis of machine learning approximations and formalisation of symmetries.
result Ricci-flat metrics have more symmetries than the underlying manifold, leading to compact representations.
Variational inference struggles with weight symmetries in neural networks, leading to biased posteriors.
problem Weight space symmetries in neural networks cause multimodal posteriors, challenging variational inference.
method Developed a symmetrization mechanism to create permutation invariant variational posteriors.
result Symmetrized variational posteriors have a better fit to the true posterior and improved predictive performance.
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.
Symmetry helps VI recover certain statistics.
problem Understanding how symmetry in variational inference affects the recovery of statistics.
method Developed a general theory of symmetry-induced statistic recovery in variational inference.
result Symmetry can force the recovery of certain statistics in VI, even under model misspecification.
This work provides statistical guarantees for GANs that are invariant to certain group symmetries.
problem Learning group-invariant distributions efficiently.
method Study of group-invariant GANs and their performance guarantees.
result Group-invariant GANs require fewer samples and have a reduced discriminator approximation error.
Probing the effects of broken symmetries in machine learningphysics.chem-ph
A machine learning model with approximate rotational symmetry is tested and found stable.
problem The effects of broken symmetries in machine learning models.
method Testing a model with approximate rotational symmetry in various physical scenarios.
result The model remains stable even with noticeable symmetry artifacts, suggesting potential benefits.
Verified numerics prove existence of a curvature solution with known symmetries.
problem Existence of a curvature solution for the Nirenberg problem.
method Verified numerics and computer assistance.
result Existence of a genuine solution with known symmetry groups.
Expands MFGs to handle real-world asymmetric multi-agent games efficiently.
problem Applying mean-field games to real-world, heterogeneous multi-agent systems.
method Develops a method to symmetrize and extend finite-player games to infinite-player MFGs, proving approximation bounds and convergence guarantees.
result TD learning converges to approximate Nash equilibria in finite-sample settings, enabling symmetrized learning without explicit MFG models.
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…
An impossibility result shows limitations in learning symmetries and equivariant functions.
problem Learning symmetries and equivariant functions simultaneously is impossible under certain conditions.
method Careful study of approximation for groups and semigroups, analysis of neural networks.
result Linearly equivariant networks can be used to learn equivariant functions, but group-convolutional networks have limitations.
We develop variational integrators from discrete Hamiltonian systems with external forces.
problem Creating accurate discrete models of continuous Hamiltonian systems.
method Constructing discrete Hamiltonian systems with external forces, analyzing symplectic structure, and combining methods to build variational integrators.
result We derive variational integrators that approximate continuous Hamiltonian systems with high accuracy.
New method uses scalars to approximate physics functions.
problem Designing neural networks that respect physical symmetries.
method Parameterizing polynomial functions equivariant to various symmetries using scalars.
result Universal approximation of polynomial functions under various symmetries using scalars.
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.
New scalable GP approximation using Fourier series decomposition.
problem Scalability and accuracy in Gaussian process approximations.
method Harmonic kernel decomposition (HKD) to decompose kernels orthogonally.
result Significantly outperforms standard variational methods in scalability and accuracy.
New method discovers symmetries in differential equations from data.
problem Directly identifying Lie symmetries from scattered data without explicit equations.
method Numerical scheme using manifold learning and linear system construction.
result Accuracy and robustness demonstrated in various differential equations.
We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be reduced resulting in compact representations of shape and spatial structure. Th…
Develops tests for conditional symmetry under group actions.
problem Testing conditional symmetry in distributions under group actions.
method Nonparametric randomization tests with kernel methods and asymptotic consistency.
result Tests achieve finite-sample Type I error control and power.
Data augmentation can achieve the same statistical benefits as full augmentation up to an approximation error.
problem Data augmentation in learning problems
method Using Fourier analysis and representation theory of finite groups
result Partial data augmentation achieves the same minimax rates as full augmentation
Coarse-Graining Hamiltonian Systems Using WSINDyphysics.comp-ph
WSINDy identifies reduced Hamiltonian systems from particle interactions.
problem Coarse-graining Hamiltonian dynamics with approximate symmetries.
method WSINDy algorithm applied to Hamiltonian systems with timescale separation.
result WSINDy successfully identifies reduced Hamiltonian systems from noisy data.
This work tackles Bayesian neural networks by addressing loss landscape symmetries.
problem Understanding and optimizing the loss landscape of Bayesian neural networks.
method The approach involves extending marginalized loss barrier formalism to BNNs, proposing a matching algorithm to search for linearly connected solutions using permutation matrices and combinatorial optimization.
result Nearly zero marginalized loss barriers for linearly connected solutions were found.
Variational Inference in Location-Scale Families: Exact Recovery of the Mean and Correlation Matrixstat.ML
Paper analyzes VI for location-scale families, proving robustness guarantees for mean and correlation recovery.
problem Misspecification in VI for intractable target densities.
method Variational inference on location-scale families with symmetries.
result VI recovers mean and correlation matrix under specific symmetries.
Automatically learns flexible symmetry constraints in neural networks using gradients.
problem Fixed hard constraints on neural network functions that cannot be adapted.
method Improves parameterisations of soft equivariance and optimizes marginal likelihood using differentiable Laplace approximations.
result Achieves equivalent or improved performance on image classification tasks compared to baselines with hard-coded symmetry.
New equations use Pin(2) symmetry to study spinor and connection solutions.
problem Study of spinor and connection solutions on 4-manifolds.
method Define and analyze Seiberg-Witten-like equations with Rarita-Schwinger operators.
result Moduli space of solutions is non-compact and non-empty under certain conditions.
Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networkscond-mat.stat-mech
New method makes machine learning approximations unbiased and efficient.
problem Efficient sampling of complex probability distributions.
method Uses autoregressive neural networks with cluster updates and physical symmetries.
result Shows unbiased and low-variance approximations for phase transitions.
In this paper, we apply the method of approximate transformation groups proposed by Baikov, Gaziziv and Ibragimov, to compute the first-order approximate symmetry for the Gardner equations with the small parameters. We compute the optimal system and analyze some invariant solutions of These types of equations. Particul…
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.
A variety of lifted inference algorithms, which exploit model symmetry to reduce computational cost, have been proposed to render inference tractable in probabilistic relational models. Most existing lifted inference algorithms operate only over discrete domains or continuous domains with restricted potential functions…
Equivariant CNNs improve RL performance in symmetric environments.
problem Learning equivariant representations for RL in symmetric environments.
method Proposed and studied equivariant CNNs for RL.
result Equivariant CNNs enhance RL performance and sample efficiency.
We review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's overdetermined problem) and for rigidity problems in geometric analysis (like Alexandrov soap bubble Theorem), and we give an overview of some r…
The purpose of this paper is to synthesize the approaches taken by Chatterjee-Meckes and Reinert-Röllin in adapting Stein's method of exchangeable pairs for multivariate normal approximation. The more general linear regression condition of Reinert-Röllin allows for wider applicability of the method, while the method of…
Symetric Monopolesmath.DG
We discuss Bogomolny monopoles of arbitrary charge invariant under various symmetry groups. The analysis is largely in terms of the spectral curves, the rational maps, and the Nahm equations associated with monopoles. We consider monopoles invariant under inversion in a plane, monopoles with cyclic symmetry…
New equivariant filters improve graph classification.
problem Designing deep learning models for graph symmetries.
method Nonlinear spectral filters (NLSFs) that are equivariant to graph functional shifts.
result NLSFs outperform existing spectral GNNs in graph classification.
Approximate Hamiltonian Symmetry Groups and Recursion Operators for Perturbed Evolution Equationsmath.AP
In this paper, the method of approximate transformation groups which was proposed by Baikov, Gazizov and Ibragimov, is extended on Hamiltonian and bi-Hamiltonian systems of evolution equations. Indeed, as a main consequence, this extended procedure is applied in order to compute the approximate conservation laws and ap…
Develops SymGCP for tensor decompositions with general symmetry.
problem Handling symmetry in tensor decompositions for better model accuracy.
method Introduces SymGCP, a generalized CP decomposition that accounts for any subset of tensor modes' symmetry.
result SymGCP enables efficient and scalable tensor decomposition with improved model robustness and accuracy.
This work connects symmetries and conserved quantities in machine learning.
problem Improving machine learning models by learning conserved quantities.
method Using Noether's theorem, learn symmetries and conserved quantities directly from data.
result Correctly identifies conserved quantities and improves model performance.