arXiv research

The paper introduces a method for creating short proofs of predictions in AI models.

Hollow-tree Super resolves feature importance in large datasets.

Estimates how many times a star appears due to gravitational lensing.

New star-shaped acceptability indexes generalize existing methods.

Study tunnel numbers of cable knots and their companions, proving new bounds and constructing examples.

The study counts geodesics on curved surfaces with specific intersections.

This paper is devoted to an inverse Steklov problem for a particular class of n-dimensional manifolds having the topology of a hollow sphere and equipped with a warped product metric. We prove that the knowledge of the Steklov spectrum determines uniquely the associated warping function up to a natural invariance.

This paper achieves first-order regret bounds in reinforcement learning with large state spaces.

We study the classical problem of maximizing a monotone submodular function subject to a cardinality constraint k, with two additional twists: (i) elements arrive in a streaming fashion, and (ii) m items from the algorithm's memory are removed after the stream is finished. We develop a robust submodular algorithm STAR-…

Paper solves Serrin problem for ring-shaped domains, showing velocity has finitely many maxima.

Paper characterizes star-shaped risk measures and their properties.

New algorithm minimizes regret in sparse reinforcement learning.

New algorithm for robust density estimation in corrupted data.

In discrete differential geometry, it is widely believed that the discrete Gaussian curvature of a polyhedral vertex star equals the algebraic area of its Gauss image. However, no complete proof has yet been described. We present an elementary proof in which we compare, for a particular normal vector, its winding numbe…

New operators help focus on specific areas in complex math problems.

We introduce a method to design lightweight shell objects that are structurally robust under the external forces they may experience during use. Given an input 3D model and a general description of the external forces, our algorithm generates a structurally-sound minimum weight shell object. Our approach works by alter…

New method robust to semi-random sparse recovery, nearly-linear time.

The paper defines new polynomials for links and linkoids.

Develops an ℓ_p theory for PCA and spectral clustering.

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with dimension-independent error guarantees for several families of structured distributions…

Proposes an efficient alternative to nonconvex-nonconcave min-max optimization.

The study shows infinitely many Reeb orbits on star-shaped hypersurfaces with growth rate like prime numbers.

We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation $\mathfrak{X}$ of the sum of an approximately) low rank matrix $Θ^\star$ with a second matrix $Γ^\star$ endowed with a complementary …

We are going to use the Euler's vector fields in order to show that for real quasi-homogeneous singularities with isolated critical value, the Milnor's fibration in a "thin" hollowed tube involving the zero level and the fibration in the complement of "link" in sphere are equivalents, since they exist. Moreover, in ord…

Let c be a periodic Reeb orbit on the boundary S of a compact star-shaped domain C in R4. We show that if there is an immersed symplectic disc f in C with boundary c then the self-linking number lk(c) of c equals 2 tan(f)-1 where tan(f) is the tangential self-intersection number of f. We also show that if C is convex a…

Let $\{{\cdot},{\cdot}\}_{\boldsymbol{\mathcal{P}}}$ be a variational Poisson bracket in a field model on an affine bundle $π$ over an affine base manifold $M^m$. Denote by $\times$ the commutative associative multiplication in the Poisson algebra $\boldsymbol{\mathcal{A}}$ of local functionals $Γ(π)\to\Bbbk$ that take…

Improved guarantees for nonconvex matrix factorization with rank overparameterization.

The paper explores graphons of line graphs from sparse finite graphs.

Introduces Star-Shaped deviation measures for risk analysis.

The study proves that in normal tilings, at least two vertices are required per cell.

The goal of this study is to present the development of a machine learning based approach that utilizes phase space alone to separate the Gaia DR2 stars into two categories: those accreted onto the Milky Way from those that are in situ. Traditional selection methods that have been used to identify accreted stars typica…

Algorithm achieves optimal regret for unknown Lipschitz convex losses.

We calculated the cross correlations between the half-hourly times series of the ten Dow Jones US economic sectors over the period February 2000 to August 2008, the two-year intervals 2002--2003, 2004--2005, 2008--2009, and also over 11 segments within the present financial crisis, to construct minimal spanning trees (…

Minimizing a convex, quadratic objective of the form $f_{\mathbf{A},\mathbf{b}}(x) := \frac{1}{2}x^\top \mathbf{A} x - \langle \mathbf{b}, x \rangle$ for $\mathbf{A} \succ 0$ is a fundamental problem in machine learning and optimization. In this work, we prove gradient-query complexity lower bounds for minimizing conv…

Paper proves conjecture about star-shaped curves evolving under GAPF, but not always preserves star shape.

New algorithm improves heteroskedastic PCA performance.

In this article, we introduce the notion of star-Ricci tensors in the real hypersurfaces of complex quadric $Q^m$. It is proved that there exist no Hopf hypersurfaces in $Q^m,m\geq3$, with commuting star-Ricci tensor or parallel star-Ricci tensor. As a generalization of star-Einstein metric, star-Ricci solitons on $M$ …

Optimal scheme minimizes deviation in federated transfer learning for kernel regression.

Classifies star products on Lie algebroid duals and extends to projectable quantizations.

New set-valued star-shaped risk measures introduced for better risk assessment.

We study Veech groups of covering surfaces of primitive translation surfaces. Therefore we define congruence subgroups in Veech groups of primitive translation surfaces using their action on the homology with entries in $\mathbb{Z}/a\mathbb{Z}$. We introduce a congruence level definition and a property of a primitive t…

Flow turns star-shaped curves into circles.

The paper studies dynamic star-shaped risk measures and their representation.

Paper disproves symmetry of stars at infinity in a specific graph.

Study star products on Poisson manifolds compatible with reduction.

The paper characterizes dynamic return and star-shaped risk measures via BSDEs.

Gradient descent learns over-param neural nets better than NTK.

Deform moment map on symplectic connections using star product algebras.