Upper bound for Laplacian eigenvalue via conformal volume.
problem Finding upper bounds for Laplacian eigenvalues.
method Using conformal volume to derive an upper bound.
result Effective upper bound for Laplacian eigenvalues on manifolds.
Upper bounds for volume spectrum depend on volume, dimension, and a conformal invariant.
problem Bounding the volume spectrum of Riemannian manifolds.
method Proves upper bounds that depend on volume, dimension, and a conformal invariant.
result Upper bounds for the volume spectrum are established.
This paper analyzes regret bounds for Gaussian process Thompson sampling.
problem Analyzing the performance of Gaussian process Thompson sampling (GP-TS) in Bayesian optimization.
method The paper derives several regret bounds for GP-TS, including a lower bound, upper bounds on the second moment of cumulative regret, expected lenient regret, and improved cumulative regret.
result The paper provides improved regret upper bounds for GP-TS, showing that it suffers from a polynomial dependence on 1 / δ 1/δ 1/ δ with probability δ δ δ . Upper bounds for CV errors apply to lasso and other models.
problem Bounding CV errors for lasso and similar models.
method Rademacher complexity and Orlicz- Ψ ν Ψ_ν Ψ ν norm. result Upper bounds are tight and stable for lasso.
We show that any space with a positive upper curvature bound has in a small neighborhood of any point a closely related metric with a negative upper curvature bound.
New upper bound for Neumann Laplacian eigenvalues on convex domains.
problem Bounding Neumann eigenvalues on convex domains.
method Deriving a new upper bound for eigenvalues.
result Universal inequalities for Neumann eigenvalues derived from the upper bound.
Sharp upper bounds found for Steklov eigenvalues of a specific hypersurface.
problem Finding upper bounds for Steklov eigenvalues of a specific type of hypersurface.
method Analytical approach to compute upper bounds and prove stability properties.
result Sharp upper bounds B n ( L ) B_n(L) B n ( L ) and B n B_n B n for Steklov eigenvalues are derived. Study proves upper bounds for solutions on Riemannian manifolds.
problem Proving upper bounds for solutions of Leibenson's equation on Riemannian manifolds.
method Proved upper bounds equivalent to a euclidean-type Sobolev inequality.
result Upper bounds for solutions of Leibenson's equation on Riemannian manifolds are equivalent to euclidean-type Sobolev inequalities.
New method improves adversarial training robustness.
problem Lack of tight upper bounds for adversarial training.
method Holistic expansion of the network for upper bound minimization.
result RUB and aRUB methods are more robust than state-of-the-art methods.
Upper bounds for Steklov eigenvalues derived from intersection indices.
problem Finding upper bounds for Steklov eigenvalues of submanifolds in Euclidean space.
method Using intersection indices of submanifolds and their boundaries.
result Explicit upper bounds involving intersection index, volume, and dimensional constants.
Upper bounds for Steklov eigenvalues of warped products are derived.
problem Finding upper limits for Steklov eigenvalues of warped product manifolds.
method Using volume, boundary volume, fiber Laplace eigenvalues, and warping function norms.
result Optimal upper bounds and stability estimates for eigenvalues are obtained.
Upper bound for conjugate radius in open manifolds with scalar curvature and spectrum constraints.
problem Bounding the conjugate radius of open manifolds with specific curvature and spectrum conditions.
method Established an upper bound using scalar curvature and bottom-of-spectrum constraints.
result For certain conditions, the conjugate radius is no more than π.
Upper bound on geodesic ball volume in Riemannian manifolds.
problem Bounding geodesic ball volume in Riemannian manifolds.
method Techniques to provide an upper bound on geodesic ball volume.
result Upper bound on geodesic ball volume in Euclidean space.
We obtain upper bounds for the eigenvalues of the Schrödinger operator L = Δ g + q L=Δ_g+q L = Δ g + q depending on integral quantities of the potential q q q and a conformal invariant called the min-conformal volume. Moreover, when the Schrödinger operator L L L is positive, integral quantities of q q q which appear in upper bounds, can be repla…
New examples show no upper bounds on link volumes on incompressible surfaces.
problem Finding upper bounds on volumes of links on incompressible surfaces.
method Examined weakly generalised alternating and fully augmented links on incompressible surfaces.
result Found infinite families of links on incompressible surfaces with no upper bounds on volume.
Let M {\mathfrak M} M be a closed, orientable, hyperbolic 3-orbifold such that π 1 ( M ) π_1({\mathfrak M}) π 1 ( M ) contains no hyperbolic triangle group. We show that strict upper bounds of 0.07625, 0.1525 and 0.22875 for v o l M {\rm vol}\ {\mathfrak M} vol M imply respective upper bounds of 23, 43 and 79 for $\dim H_1({\mathfrak M};{\mathbb F}_2…
Upper bounds found for systole function critical points on surface moduli space.
problem Finding upper bounds for systole function critical points.
method Analyzing the systole function on the surface moduli space.
result Upper bounds for critical points of systole function and their systole values.
We prove global and local upper bounds for the Hessian of log positive solutions of the heat equation on a Riemannian manifold. The metric is either fixed or evolves under the Ricci flow. These upper bounds supplement the well-known global lower bound.
The paper honors Lai's contributions to multi-armed bandits and establishes new regret bounds.
problem Improving regret bounds in multi-armed bandit problems.
method Establishes non-asymptotic regret bounds for upper confidence bound indices.
result New regret bounds match Lai-Robbins lower bound.
Upper bounds for Steklov eigenvalues on curved submanifolds.
problem Eigenvalue bounds for Steklov problem on submanifolds.
method Reilly-type upper bounds for p p p -Steklov eigenvalues. result Proved upper bounds for the first non-zero eigenvalue.
Upper bounds for eigenvalues on submanifolds in weighted manifolds.
problem Eigenvalue bounds for submanifolds in weighted Riemannian manifolds.
method Proving upper bounds for divergence-type operators and Steklov problems on submanifolds.
result Reilly-type upper bounds for eigenvalues.
Paper presents a reduction-based framework for conservative bandits and RL with improved lower and upper bounds.
problem Conservative bandits and reinforcement learning problems.
method Reduction technique to calculate necessary and sufficient budget from baseline policy.
result Improved lower and upper bounds for various conservative settings.
Characterizes orbifolds with upper curvature bounds as reflectofolds.
problem Understanding orbifolds with upper curvature bounds.
method Characterization through Alexandrov curvature and reflectofolds.
result Quotients of Riemannian manifolds by isometries have locally bounded curvature if and only if they are reflectofolds.
Study bounds growth rate of irreducible meanders, showing proportion vanishes.
problem Understanding growth rate of irreducible meanders.
method Provided upper and lower bounds for growth rate.
result Proportion of irreducible meanders among prime meanders approaches 0 as n increases.
A new method to measure neural network expressiveness using tighter upper bounds.
problem Measuring the expressiveness of deep neural networks (DNNs).
method Proposes a new tighter upper bound for the number of linear regions in rectifier networks, using matrix computation.
result The proposed upper bound is tighter than existing ones and explains the performance improvements of skip connections and residual structures.
Sharp upper bound found for Steklov spectrum on revolution submanifolds.
problem Finding bounds for Steklov spectrum on specific submanifolds.
method Analyzing submanifolds of revolution in Euclidean space.
result Sharp upper bound established for Steklov spectrum.
Stochastic variational inference (SVI) plays a key role in Bayesian deep learning. Recently various divergences have been proposed to design the surrogate loss for variational inference. We present a simple upper bound of the evidence as the surrogate loss. This evidence upper bound (EUBO) equals to the log marginal li…
Theorems prove upper bounds for foliations on closed Alexandrov spaces.
problem Upper bounds for the dimension of isometry groups of metric foliations.
method Proving theorems about isometries and foliations on closed Alexandrov spaces.
result Sharp upper bounds for the dimension of the isometry group of metric foliations.
Upper bound for Morse index of min-max varifolds.
problem Bounding Morse index of varifolds.
method Proving upper bound for Morse index of min-max stationary integral varifolds.
result Upper bound for Morse index of min-max stationary integral varifolds.
Upper bound found for Steklov eigenvalue of a surface of revolution.
problem Finding an upper limit for Steklov eigenvalues of a specific surface.
method Analyzing a surface of revolution with boundary conditions of two spheres.
result An upper bound for the first Steklov eigenvalue is derived and shown to be sharp in some cases.
Upper bounds found for eigenvalues of weighted Steklov and (p,q)-Laplacian problems.
problem Finding upper bounds for eigenvalues of weighted Steklov and (p,q)-Laplacian problems.
method Proving upper bounds using the weighted p-Laplace operator and ( p , q ) (p,q) ( p , q ) -Laplacian on submanifolds. result Reilly-type upper bounds for the first eigenvalues of Steklov and (p,q)-Laplacian problems.
Improved bounds on combining hypothesis classes for binary functions.
problem Understanding how to combine hypothesis classes for binary functions.
method Established upper bounds on Littlestone and threshold dimensions for combined classes.
result Upper bounds are nearly tight and give exponential improvements.
We use spectral embeddings to give upper bounds on the spectral function of the Laplace--Beltrami operator on homogeneous spaces in terms of the volume growth of balls. In the case of compact manifolds, our bounds extend the 1980 lower bound of Peter Li for the smallest positive eigenvalue to all eigenvalues. We also i…
Paper improves upper bound for torus eigenvalues.
problem Maximizing the second non-zero Laplace eigenvalue on tori.
method New upper bound derived for flat tori, applied to general tori.
result Improved upper bound for λ 2 ( T a , b , g ) λ_2(T_{a, b},g) λ 2 ( T a , b , g ) on flat tori. The study finds polynomial upper bounds for singularities in Einstein-scalar field system.
problem Understanding the strength of singularities in gravitational collapse.
method Analyzing geometric quantities, focusing on the Kretschmann scalar.
result Polynomial blow-up upper bounds O ( 1 / r N ) O(1/r^N) O ( 1/ r N ) for the Kretschmann scalar, improving previous bounds. New bounds for Bayesian bandits show prior improves performance.
problem Improving regret bounds for Bayesian bandits.
method Upper confidence bound algorithm with finite-time logarithmic regret bounds.
result Derives O ( c Δ log n ) O(c_Δ\log n) O ( c Δ log n ) and O ( c h log 2 n ) O(c_h \log^2 n) O ( c h log 2 n ) upper bounds for Bayesian bandits. Study sets a nontrivial upper limit on return forecasting accuracy.
problem Establishing a practical upper limit for return forecasting accuracy.
method Defined a coin-flip oracle model to theoretically outperform practical models and used its R e x t O O S 2 R^2_{ ext{OOS}} R e x t O O S 2 as an upper bound. result Theoretical upper bound on R e x t O O S 2 R^2_{ ext{OOS}} R e x t O O S 2 is a quadratic function of directional accuracy. Paper improves regret bounds for Gaussian process upper confidence bound in Bayesian optimization.
problem Minimizing regret in Gaussian process bandit optimization.
method Gaussian process upper confidence bound (GP-UCB) algorithm with refined analysis.
result Achieves O ( T ln 2 T ) O(\sqrt{T \ln^2 T}) O ( T ln 2 T ) cumulative regret under squared exponential kernel. Improved upper bound on superbridge index from 5b-3 to 3b-1.
problem Improving bounds on superbridge index for knots.
method Improved upper bound formula for superbridge index.
result Upper bound on superbridge index reduced from 5b-3 to 3b-1.
Knotted ribbons form an important topic in knot theory. They have applications in natural sciences, such as cyclic duplex DNA modeling. A flat knotted ribbon can be obtained by gently pulling a knotted ribbon tight so that it becomes flat and folded. An important problem in knot theory is to study the minimal ratio of …
New bounds on continuous random variables' right-tail probabilities.
problem Finding precise upper and lower limits for right-tail probabilities of continuous random variables.
method Developed new bounds based on PDF, first derivative, and two parameters.
result The new bounds are tight for various continuous random variables.
We extend Bayes' theorem for upper probabilities considering likelihood uncertainty.
problem Addressing uncertainty in likelihood for upper probability bounds.
method Generalization of Wasserman and Kadane's result, considering both prior and likelihood uncertainty.
result A sufficient condition for the upper bound to become an equality.
We give a characterization of critical points that allows us to define a metric invariant on all Riemannian manifolds M M M with a lower sectional curvature bound and an upper radius bound. We show there is a uniform upper volume bound for all such manifolds with an upper bound on this invariant. We generalize results by…
We establish upper bounds for the complexity of Seifert fibered manifolds with nonempty boundary. In particular, we obtain potentially sharp bounds on the complexity of torus knot complements.
New method improves understanding of machine learning model performance.
problem Understanding how well machine learning models generalize from training data to unseen data.
method Auxiliary Distribution Method to derive new generalization error bounds.
result Upper bounds on generalization errors are tighter and more applicable.
Improved algorithm for modular links provides upper volume bounds.
problem Understanding the geometry of modular links and Lorenz links.
method Bunch algorithm to study modular links and provide upper volume bounds.
result First upper volume bound independent of word exponents and quadratic in braid index.
We give (1) an upper bound on the denominators of numerical boundary slopes and (2) an upper bound on the differences between two numerical boundary slopes, for Montesinos knot exteriors.
In this paper, we will present some characterizations for the upper bound of the Bakry-Emery curvature on a Riemannian manifold by using functional inequalities on path space. Moreover, some characterizations for general lower and upper bounds of Ricci curvature are also given, which extends the recent results derived …