arXiv research

Proves gap rigidity theorem for Hermitian symmetric spaces.

New methods reduce bias in estimating optimality gaps for risk-averse stochastic programs.

The paper explores gaps in curvature-related metrics and rigidity.

New conditions prevent gaps in optimal control problems.

Study simplicial volume for fixed fundamental groups, finding gaps.

GSP improves global average pooling for deep metric learning by learning weights and selecting semantic entities.

Study gap-dependent regret bounds for risk-sensitive RL.

Paper proves Simon's third gap conjecture for minimal surfaces in spheres.

Solves clustering contradictions by high-dimensional embedding with wide gaps.

Sharp spectral gap estimates for higher-order operators on hyperbolic spaces.

Optimal privacy-preserving algorithm for solving saddle point problems.

Counterexample shows state-constrained optimal control problems can have Young measure gaps.

We show a sharp conformally invariant gap theorem for Yang-Mills connections in dimension 4 by exploiting an associated Yamabe-type problem.

Computing unlinking number is usually very difficult and complex problem, therefore we define BJ-unlinking number and recall Bernhard-Jablan conjecture stating that the classical unknotting/unlinking number is equal to the BJ-unlinking number. We compute BJ-unlinking number for various families of knots and links for w…

The article proves a conjecture about the fundamental gap for horoconvex domains in hyperbolic space.

In our previous work "Characterization of certain homorphic geodesic cycles on Hermitian locally symmetric manifolds of the noncompact type" in "Modern methods in Complex Analysis" Annals of Math. Studies 138 (1995) 85-118, we formulated a conjecture: the so called "gap phenomenon". The purpose of the article is two-fo…

This paper studies eigenvalues of the clamped plate problem on a bounded domain in an $n$-dimensional Euclidean space. We give an estimate for the gap between $\sqrt {Γ_{k+1}-Γ_{1}}$ and $\sqrt {Γ_{k}-Γ_{1}}$, for any positive integer $k$. According to the asymptotic formula of Agmon and Pleijel, we know, the gap betwe…

Adapting the method of Andrews-Clutterbuck we prove an eigenvalue gap theorem for a class of non symmetric second order linear elliptic operators on a convex domain in euclidean space. The class of operators includes the Bakry-Emery laplacian with potential and any operator with second order term the laplacian whose fi…

Proves a fundamental gap lower bound for horoconvex domains in hyperbolic space.

Probabilistic method proves gap estimates on sphere.

This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programm…

Foundation models improve wage gap decomposition by capturing omitted career history factors.

This paper develops several average-case reduction techniques to show new hardness results for three central high-dimensional statistics problems, implying a statistical-computational gap induced by robustness, a detection-recovery gap and a universality principle for these gaps. A main feature of our approach is to ma…

Paper tackles fast convergence for non-convex strongly-concave min-max problems.

Study rigidity of spectral gap on Finsler manifolds with specific curvature bounds.

We consider the problem of estimating from sample paths the absolute spectral gap $γ_*$ of a reversible, irreducible and aperiodic Markov chain $(X_t)_{t \in \mathbb{N}}$ over a finite state space $Ω$. We propose the ${\tt UCPI}$ (Upper Confidence Power Iteration) algorithm for this problem, a low-complexity algorithm …

Study concavity of solutions to elliptic equations under conformal deformations.

Study analyzes symmetric two-armed Bernoulli bandit problem with zero mean gap.

New computational lower bounds for clustering and related problems.

MO-GP models fill gaps in biophysical data with across-domain info transfer.

New framework for RL with linear-convex models reduces performance gap.

Estimates scalar curvature without nonnegativity, showing gap phenomenon on manifolds.

Solves the Wiegold problem by showing free products of left-orderable groups have normal rank > 1.

We propose two methods for exact Gaussian process (GP) inference and learning on massive image, video, spatial-temporal, or multi-output datasets with missing values (or "gaps") in the observed responses. The first method ignores the gaps using sparse selection matrices and a highly effective low-rank preconditioner is…

This paper studies the problem of adaptively sampling from K distributions (arms) in order to identify the largest gap between any two adjacent means. We call this the MaxGap-bandit problem. This problem arises naturally in approximate ranking, noisy sorting, outlier detection, and top-arm identification in bandits. Th…

Solves approximation problems for zonoids and neural networks, closing gaps in dimensions 2 and 3.

In these notes we describe heuristics to predict computational-to-statistical gaps in certain statistical problems. These are regimes in which the underlying statistical problem is information-theoretically possible although no efficient algorithm exists, rendering the problem essentially unsolvable for large instances…

This paper bridges the gap between theoretical and practical OPE for bandit problems.

Optimal strategy found for identifying best arm in bandits with small gap.

Detection of dense cycles in graphs reveals a gap between easy detection and hard recovery.

UCB algorithm's arm-sampling behavior is revealed, leading to new insights and proofs.

Paper closes the gap in MP-MAB problems with novel adaptive communication and exploration.

A novel method detects multiple mitosis events and mitigates annotation gaps in phase-contrast microscopy.

The paper explains what affects the generalization gap in visual RL with and without distractors.

A new neural network model predicts inflation and output gap more accurately.

Several recently proposed architectures of neural networks such as ResNeXt, Inception, Xception, SqueezeNet and Wide ResNet are based on the designing idea of having multiple branches and have demonstrated improved performance in many applications. We show that one cause for such success is due to the fact that the mul…

In this paper, we investigate the Dirichlet problem of Laplacian on complete Riemannian manifolds. By constructing new trial functions, we obtain a sharp upper bound of the gap of the consecutive eigenvalues in the sense of the order, which affirmatively answers to a conjecture proposed by Chen-Zheng-Yang. In addition,…

Unified framework for CO problems using RL, providing optimal solutions and convergence guarantees.