arXiv research

Study on flat connections with controlled irregularity.

New bounds for score matching in polynomial exponential families.

New bounds on Khovanov homology for positive links families.

We show that $\mathbb{Q}$-Fano varieties of fixed dimension with anti-canonical degrees and alpha-invariants bounded from below form a bounded family. As a corollary, K-semistable $\mathbb{Q}$-Fano varieties of fixed dimension with anti-canonical degrees bounded from below form a bounded family.

New insights into natural exponential families improve regret bounds for bandit problems.

In recent years, several families of hyperbolic knots have been shown to have both volume and $λ_1$ (first eigenvalue of the Laplacian) bounded in terms of the twist number of a diagram, while other families of knots have volume bounded by a generalized twist number. We show that for general knots, neither the twist nu…

The paper studies families of curves on surfaces that realize all types of pants decompositions.

New examples show no upper bounds on link volumes on incompressible surfaces.

The study provides a generalization bound for a family of implicit networks.

Unified framework for understanding TVO and improving model learning.

Sharp lower bounds for modular invariants and Dehn twist coefficients in genus 2 and 3.

Bounds on geodesic distances on Stiefel manifold derived from new metrics.

New separation concepts for Anosov representations help bound Thurston asymmetric metric.

In this paper we obtain a bound on the number of isometry classes of finite area hyperbolic surfaces which are length isospectral to a given surface depending only on the topological type of the surface and the length of the shortest closed geodesic on the surface. This will follow from a more general bound applying to…

Paper proves all Lagrangians unobstructed if one is, using non-archimedean analytic structure.

In the present paper, we consider the family of all compact Alexandrov spaces with curvature bound below having a definite upper diameter bound of a fixed dimension. We introduce the notion of essential coverings by contractible metric balls, and provide a uniform bound on the numbers of contractible metric balls formi…

We first show that a Laplace isospectral family of Riemannian orbifolds, satisfying a lower Ricci curvature bound, contains orbifolds with points of only finitely many isotropy types. If we restrict our attention to orbifolds with only isolated singularities, and assume a lower sectional curvature bound, then the numbe…

New homomorphism from Khovanov homology gives slice genus bounds.

Proposes a general method to derive regret bounds for multi-armed bandit algorithms.

We show that dropout training is best understood as performing MAP estimation concurrently for a family of conditional models whose objectives are themselves lower bounded by the original dropout objective. This discovery allows us to pick any model from this family after training, which leads to a substantial improvem…

Paper improves generalization bounds for noisy stochastic algorithms.

Bounds on conformal dimension for certain Coxeter group boundaries.

New 3-manifolds bound rational 4-balls through specific operations.

For families of knots and links given in Conway notation we compute lower maximal and upper minimal bound of hyperbolic volume by using source links and augmented links.

New bounds for knot complexity based on Jones polynomial coefficients.

Paper finds infinite family of minimal triangulations for complex 3D shapes.

SMRL uses score matching for efficient RL with exponential family models.

Approximates cycles in planar and bounded-genus graphs.

When choosing the right copula for our data a key point is to distinguish the family that describes it at the best. In this respect, a better choice of the copulas could be obtained through the information about the (non)symmetry of the data. Exchangeability as a probability concept (first next to independence) has bee…

In his work on the Farrell-Jones Conjecture, Arthur Bartels introduced the concept of a "finitely $\mathcal{F}$-amenable" group action, where $\mathcal{F}$ is a family of subgroups. We show how a finitely $\mathcal{F}$-amenable action of a countable group $G$ on a compact metric space, where the asymptotic dimensions o…

New clustering method for exponential family data.

For each rational homology 3-sphere $Y$ which bounds simply connected definite 4-manifolds of both signs, we construct an infinite family of irreducible rational homology 3-spheres which are homology cobordant to $Y$ but cannot bound any simply connected definite 4-manifold. As a corollary, for any coprime integers $p,…

In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary kernels, and propose a family of spectral kernels that extends existing approac…

In this paper, we show that the volumes for a family of A-adequate closed braids can be bounded above and below in terms of the twist number, the number of braid strings, and a quantity that can be read from the combinatorics of a given closed braid diagram. We also show that the volumes for many of these closed braids…

Upper bound conjecture for Yokota invariant proved for polyhedral graphs.

In this paper we consider three arithmetic families of isospectral non-isometric Riemannian orbifolds and in each case derive an upper bound for the size of the family which is polynomial as a function of the volume of the orbifolds. The first family that we consider are those constructed by Vigneras' method. The secon…

New examples of Kirby-Ramanujam spheres found, leading to contractible 4-manifolds.

Twisted torus knots and links are given by twisting adjacent strands of a torus link. They are geometrically simple and contain many examples of the smallest volume hyperbolic knots. Many are also Lorenz links. We study the geometry of twisted torus links and related generalizations. We determine upper bounds on their …

This article considers a one-parameter family of circles F_C, which has the interesting property that the null isocline of the family is the largest member of the family. This family of circles is bounded and we consider the problem of deriving an equation for the envelope of F_C. We provide one standard solution, and …

Semi-implicit variational inference (SIVI) is introduced to expand the commonly used analytic variational distribution family, by mixing the variational parameter with a flexible distribution. This mixing distribution can assume any density function, explicit or not, as long as independent random samples can be generat…

We define a family of link concordance invariants $\left\{ s_n \right\}_{n=2,3, \cdots}$. These link concordance invariants give lower bounds on the slice genus of a link $L$. We compute the slice genus of positive links. Moreover, these invariants give lower bounds on the link splitting number of a link. Especially, t…

Generalization bounds derived for neural ODEs and deep residual networks.

New method for tensor completion using nonconvex dual total variation.

We call an integral homology sphere $\textit{non-trivially}$ bounds a rational homology ball if it is obstructed from bounding an integral homology ball. After Fintushel and Stern's well-known example $Σ(2,3,7)$, Akbulut and Larson recently provided the first infinite families of Brieskorn spheres non-trivially boundin…

We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the Lipschitz properties of neural network family, we achieve significantly tighter g…

Analyzes the complexity of linear hypothesis sets using Rademacher complexity.

Study finds infinite families of Sasaki-Einstein metrics on spheres.

This paper describes a family of pseudo-Anosov braids with small dilatation. The smallest dilatations occurring for braids with 3, 4 and 5 strands appear in this family. A pseudo-Anosov braid with 2g+1 strands determines a hyperelliptic mapping class with the same dilatation on a genus-g surface. Penner showed that log…