New method estimates sparse canonical vectors efficiently.
problem Sparse canonical vectors estimation in CCA.
method Quasi-Bayesian estimation via Rayleigh quotient function.
result Achieves minimax rate with low computational cost.
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.
168,657 papers · 148 categories
Trend · papers per month
48 results for “Rayleigh quotient optimization”
Proposes a framework to extract ordered eigenfunctions from contextual kernels.
problem Lack of exact spectral decomposition in existing methods.
method Modular building blocks for compatibility with contextual kernels and scalability.
result Extracted eigenfunctions provide effective importance scores for feature selection.
A Geometric Analysis of PCAmath.ST
The paper analyzes the excess risk of PCA and provides a precise characterization.
problem Understanding the excess risk of principal component analysis (PCA).
method Established a central limit theorem for PCA error and derived the excess risk distribution.
result Obtained a non-asymptotic upper bound on the excess risk of PCA.
The techniques and analysis presented in this paper provide new methods to solve optimization problems posed on Riemannian manifolds. A new point of view is offered for the solution of constrained optimization problems. Some classical optimization techniques on Euclidean space are generalized to Riemannian manifolds. S…
Improved lower bound for first eigenvalue of minimal hypersurfaces in spheres.
problem Finding a tighter bound for the first eigenvalue of minimal hypersurfaces in spheres.
method Rayleigh quotient estimate for a harmonic extension of an eigenfunction.
result Proved a new lower bound for the first eigenvalue of minimal hypersurfaces in spheres.
This note proves a Gaussian version of a Pólya-Szegö conjecture using rearrangement techniques.
problem Finding the domain with the minimum Gaussian principal frequency when the Gaussian torsional rigidity is fixed.
method Adapted Kohler-Jobin rearrangement technique to the Gauss space, considering a modified torsional rigidity and rearranging layers to half-spaces.
result The Gaussian principal frequency is minimized for the half-space when the Gaussian torsional rigidity is fixed.
The paper extends a spectral evolution model for link prediction in evolving networks.
problem Link prediction in evolving networks.
method Approximated eigenvalue trajectories using Rayleigh quotient and extrapolation.
result Learning algorithms based on approximated trajectories outperform traditional methods.
Sharp-SSL: Selective high-dimensional axis-aligned random projections for semi-supervised learningstat.ME
Sharp-SSL uses random projections to identify important variables for semi-supervised learning.
problem High-dimensional semi-supervised learning problems.
method Careful aggregation of low-dimensional results from many axis-aligned random projections.
result Sharp-SSL algorithm can recover signal coordinates with high probability.
The paper develops efficient algorithms for sampling from random spanning trees and determinantal point processes.
problem Sampling from strongly Rayleigh distributions efficiently.
method Optimal sublinear sampling algorithms for random spanning trees and determinantal point processes.
result Achieves optimal sublinear sampling for strongly Rayleigh distributions.
In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a bounded domain (with smooth boundary) in a given complete (not compact a priori) Riemannian manifold with Ricci bounded below . For this, we use test functions for the Rayleigh quotient subordinated to a family of open se…
In this note we consider sampling from (non-homogeneous) strongly Rayleigh probability measures. As an important corollary, we obtain a fast mixing Markov Chain sampler for Determinantal Point Processes.
Affirm Lord Rayleigh's conjecture on curved spaces for clamped plates.
problem Lord Rayleigh's conjecture for vibrating clamped plates on curved spaces.
method Nodal-decomposition argument, Lévy-Gromov isoperimetric inequality, Gaussian hypergeometric functions, sharp spectral gap estimates.
result Positive curvature enhances genuine differences between low- and high-dimensional settings.
Study on GEPs with generative priors, showing optimal statistical rates and proposing an iterative algorithm.
problem Generalized eigenvalue problems with generative priors.
method Assumption of Lipschitz continuous generative model, Projected Rayleigh Flow Method (PRFM).
result PRFM converges linearly to an estimated vector achieving the optimal statistical rate.
Thermodynamic description of world GDP distribution over countriescond-mat.stat-mech
The world GDP distribution is described using thermodynamics principles.
problem Understanding the distribution of GDP among countries.
method Applied Rayleigh-Jeans thermalization to GDP data.
result Emergence of low GDP states similar to condensation in optics.
Convolutional and Recurrent, deep neural networks have been successful in machine learning systems for computer vision, reinforcement learning, and other allied fields. However, the robustness of such neural networks is seldom apprised, especially after high classification accuracy has been attained. In this paper, we …
In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh-Taylor sign condition holds. We prove that as the surface tension tends to zero, when the Rayleigh-Taylor condition is satisfied, solutions converge to the Euler …
Wealth Thermalization Hypothesis and Social Networkscond-mat.stat-mech
The study applies wealth thermalization hypothesis to social networks and explains inequality.
problem Explains inequality in human society through wealth thermalization hypothesis.
method Uses Random Matrix Theory and social networks with nonlinear perturbation.
result Shows that wealth distribution follows Rayleigh-Jeans distribution, leading to inequality.
The paper proves instability of translating λ-solitons and provides bounds on their length.
problem Stability of translating λ-solitons in cylindrical geometry.
method Analytical proof of instability and explicit length bounds.
result Explicit bounds on the length of unstable translating λ-solitons.
Physics-informed neural networks improve surrogate modeling of turbulent Rayleigh-Bénard convection.
problem Modeling turbulent Rayleigh-Bénard convection with high accuracy and efficiency.
method Physics-informed neural networks (PINNs) with novel padding and regularization techniques.
result Significantly improved predictive accuracy of surrogate models at high Rayleigh numbers Ra = 2 × 10^9.
The paper derives the QGS equations using stochastic central extensions.
problem Deriving the viscous quasi-geostrophic equations on the torus.
method Central extensions of Lie groups and Lie algebras, stochastic Lagrangian formulation, and Euler-Poincaré reduction.
result Stochastic perturbations to the central extension lead to solutions of the QGS equations.
Sparse generalized eigenvalue problem (GEP) plays a pivotal role in a large family of high-dimensional statistical models, including sparse Fisher's discriminant analysis, canonical correlation analysis, and sufficient dimension reduction. Sparse GEP involves solving a non-convex optimization problem. Most existing met…
Enhanced VMC methods improve neural wavefunction training.
problem Efficiently training neural wavefunctions in VMC to converge to energy minimum.
method Rayleigh-Gauss-Newton (RGN) optimization and parallel tempering sampling.
result RGN method achieves superlinear convergence with reduced computational cost.
Paper develops IFTRR to solve sparse generalized eigenvalue problems efficiently.
problem Finding the leading eigenvector with at most k nonzero entries in sparse generalized eigenvalue problems.
method Inverse-free truncated Rayleigh-Ritz method (IFTRR) with a new truncation strategy.
result IFTRR efficiently finds the support set of the leading eigenvector for large scale problems.
The paper introduces a new efficient nonlinear one-class classifier formulated as the Rayleigh quotient criterion optimisation. The method, operating in a reproducing kernel Hilbert space, minimises the scatter of target distribution along an optimal projection direction while at the same time keeping projections of po…
Depth-Efficient Quantum Topological Data Analysis for Regime-Specific Detection of Financial Stressquant-ph
Quantum method detects financial stress regimes from market data.
problem Detecting financial stress regimes from market data.
method Adapted Pauli Correlation Encoding to quantum topological data analysis.
result Quantum method can recover Betti numbers exactly at every scale.
Designing energy-efficient networks is of critical importance for enabling state-of-the-art deep learning in mobile and edge settings where the computation and energy budgets are highly limited. Recently, Liu et al. (2019) framed the search of efficient neural architectures into a continuous splitting process: it itera…
New criterion for cylinder stability in curved spaces.
problem Stability of cylinders in curved spaces.
method Extending Plateau-Rayleigh criterion to curved spaces and proving existence of instability threshold.
result Existence of a positive number for cylinder instability in spaces.
Proves existence of eigenvalue and eigenfunction for complex Monge-Ampère operator.
problem Eigenvalue problem for complex Monge-Ampère operator on bounded domains.
method Follows P.L. Lions' strategy for real case, proves new existence theorem for complex degenerate equations, uses a priori estimates and variational approach.
result Existence of first eigenvalue and eigenfunction with specified properties.
Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
problem Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
method Reformulating Stein discrepancy construction as an explicit SNR^2 maximisation problem
result Avoiding exponential SNR^2 collapse and achieving stable SNR^2
We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the Cauchy-Schwarz inequality--is used to produce ``parameter-free'', ``projection-free'' vers…
Physics-informed model reduces RBC simulation costs.
problem Computational infeasibility of direct numerical simulations for turbulent systems.
method Combines CNN and recurrent architecture, penalized with PDEs, uses conformal prediction.
result Significant reduction in computational cost for long-term simulations.
We study probability measures induced by set functions with constraints. Such measures arise in a variety of real-world settings, where prior knowledge, resource limitations, or other pragmatic considerations impose constraints. We consider the task of rapidly sampling from such constrained measures, and develop fast M…
New MIMO constellation design for noncoherent communications reduces hardware complexity.
problem Designing efficient MIMO constellations for noncoherent communications over fading channels.
method Geodesic curves of the Grassmann manifold for structured constellation design.
result Achieves comparable error performance to unstructured designs with reduced hardware complexity.
We introduce in this paper a new algorithm for Multi-Armed Bandit (MAB) problems. A machine learning paradigm popular within Cognitive Network related topics (e.g., Spectrum Sensing and Allocation). We focus on the case where the rewards are exponentially distributed, which is common when dealing with Rayleigh fading c…
We consider a column of a rotating stationary surface in Euclidean space. We obtain a value in such way that if the length of column satisfies , then the surface is instable. This extends, in some sense, previous results due to Plateau and Rayleigh for columns of surfaces with constant mean curvature…
Generalized R2R handles non-Gaussian noise for deep network training.
problem Training deep networks from noisy data alone.
method Extending R2R to handle various noise distributions.
result GR2R loss is an unbiased estimator of supervised loss.
Study stability and bifurcation of liquid interfaces in cylindrical supports.
problem Stability and bifurcation of liquid interfaces in cylindrical support surfaces.
method Analysis of eigenvalues of the Jacobi operator, Plateau-Rayleigh instability, bifurcation theory.
result Conditions for the emergence of new morphologies and bifurcations from circular cylinders.
Sharp inequalities in nonnegative Ricci curvature spaces using mass transport.
problem Proving sharp isoperimetric and Sobolev inequalities in nonnegative Ricci curvature spaces.
method Optimal mass transport theory, symmetrization techniques, and volume non-collapsing properties.
result Sharp isoperimetric and Sobolev inequalities established in Riemannian manifolds with nonnegative Ricci curvature.
New methods detect continuous variation in single-cell data.
problem Continuous variation within and between cell types not detected by discrete analyses.
method Three topologically motivated mathematical methods for unsupervised feature selection.
result Detect additional biologically meaningful genes with coherent expression patterns.
Paper computes optimal matching between curves on manifolds.
problem Matching curves on infinite-dimensional manifolds.
method Geodesic computation using Riemannian metric and quotient structure.
result Algorithm for computing geodesics in shape space.
Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) distributions such as the well-known determinantal point process. While SR distributions offer elegant models of diversity, they lac…
For a bounded domain with a piecewise smooth boundary in a complete Riemannian manifold , we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. By making use of a fact that eigenfunctions form an orthonormal basis of in place of the Rayleigh-Ritz formula, we obtain inequalities for …
Bottom of the Spectrum of Complete Kähler Metrics from Finite-Mass Plurisubharmonic Exhaustionsmath.CV
The paper studies Kähler metrics from finite Monge-Ampère mass exhaustion functions.
problem Investigating the spectrum of complete Kähler metrics from finite Monge-Ampère mass exhaustion functions.
method Analyzing logarithmic potentials and the associated complete Kähler metrics, proving bounds on the spectrum using the finite Monge-Ampère mass condition.
result The lower bound of the spectrum of the Laplace-Beltrami operator is under the finite Monge-Ampère mass condition.
Investigates diversification quotient based on VaR and ES for portfolio models.
problem Quantifying diversification of portfolios using VaR and ES.
method Introduced and analyzed DQ based on VaR and ES for elliptical and MRV distributions.
result Explicit formulas and portfolio optimization problems for VaR and ES DQ are derived.
Two-sample tests improve on existing methods for microtubule data.
problem Testing differences between two groups of filament data.
method Optimal lifts and manifold stability theorem applied to microtubule data.
result New tests outperform existing methods on simulated and real data.
Optimizes bounds for threefold singularity volumes.
problem Bounding local volumes of threefold singularities.
method Analyzes Gorenstein canonical non-hypersurface threefold singularities.
result Establishes optimal upper bound for local volumes.
Paper introduces REED for noncoherent OTA-FL, reducing latency without phase alignment.
problem Noncoherent OTA-FL requires signed model updates without phase alignment.
method Introduces REED for continuous signed aggregation using resource-element energy difference.
result Exact variance laws for REED and chip-diverse extension in Rayleigh fading.
Operator-valued formulas for Riemannian Gradient and Hessian and families of tractable metricsmath.OC
New formulas for Riemannian gradient and Hessian on manifold metrics.
problem Evaluate Riemannian gradient and Hessian for various metrics on manifolds.
method Explicit formulas derived from Levi-Civita connection and projection.
result Derives new metrics and optimization frameworks on manifolds.