arXiv research

Machine learning improves polymer design accuracy.

Extends AKSZ to poly-symplectic structures for more complex spaces.

This paper explores the limits of deep learning in poly-time.

Estimates eigenvalues of poly-Laplace operator on lattice subgraphs.

To any $\mathfrak{g}$-manifold $M$ are associated two dglas $\operatorname{tot}\big(Λ^{\bullet} \mathfrak{g}^\vee \otimes_{\Bbbk} T_{\operatorname{poly}}^{\bullet} \big)$ and $\operatorname{tot} \big(Λ^{\bullet} \mathfrak{g}^\vee\otimes_{\Bbbk} D_{\operatorname{poly}}^{\bullet} \big)$, whose cohomologies $H_{\operatorn…

In this paper we introduce poly-Poisson structures as a higher-order extension of Poisson structures. It is shown that any poly-Poisson structure is endowed with a polysymplectic foliation. It is also proved that if a Lie group acts polysymplectically on a polysymplectic manifold then, under certain regularity conditio…

In this paper we generalize the notion of strongly poly-free group to a larger class of groups, we call them strongly poly-surface groups and prove that the Fibered Isomorphism Conjecture of Farrell and Jones corresponding to the stable topological pseudoisotopy functor is true for any virtually strongly poly-surface g…

Improved lower bounds for poly-Laplacian eigenvalues in arbitrary dimensions.

We consider the adversarial convex bandit problem and we build the first $\mathrm{poly}(T)$-time algorithm with $\mathrm{poly}(n) \sqrt{T}$-regret for this problem. To do so we introduce three new ideas in the derivative-free optimization literature: (i) kernel methods, (ii) a generalization of Bernoulli convolutions, …

Poly-view contrastive learning improves image representation learning.

Poly-GNNs achieve similar performance regardless of depth, highlighting graph noise's dominance.

Graph poly-Laplacian method improves regression accuracy.

Study on maximizing submodular functions with limited updates, achieving tight bounds and poly-time algorithms.

We consider the lower order eigenvalues of poly-Laplacian with any order on spherical domains. We obtain universal inequalities for them and show that our results are optimal.

Bounds and estimates for eigenvalues of poly-harmonic and biharmonic operators.

Product formula for K-stability proved.

We develop an efficient algorithm for low-rank approximation with improved approximation guarantees.

Develops efficient algorithms for learning latent-variable models using implicit moment tensor computation.

Poly-free groups are constructed as iterated semidirect products of free groups. The class of poly-free groups includes the classical pure braid groups, fundamental groups of fiber-type hyperplane arrangements, and certain subgroups of the automorphism groups of free groups. The purpose of this article is to compute ce…

In this paper, we study eigenvalues of the poly-Laplacian with arbitrary order on a bounded domain in an n-dimensional Euclidean space and obtain a lower bound for eigenvalues, which generalizes the results due to Cheng-Wei [5] and gives an improvement of results due to Cheng- Qi-Wei [3].

In this paper, we investigate the Dirchlet eigenvalue problems of poly-Laplacian with any order and quadratic polynomial operator of the Laplacian. We give some estimates for lower bounds of the sums of their first $k$ eigenvalues which improve the previous results.

In this paper, we study eigenvalues of the poly-Laplacian with arbitrary order on a bounded domain in an $n$-dimensional Euclidean space and obtain a lower bound for eigenvalues, which gives an important improvement of results due to Levine and Protter. In particular, the result of Melas is included here.

$\newcommand{\poly}{_{\operatorname{poly}}^{\bullet}}\newcommand{\td}{(\operatorname{td}_{L/A}^{\nabla})^{\frac{1}{2}}}\newcommand{\cx}[1]{\operatorname{tot}\big(Γ(Λ^\bullet A^\vee)\otimes_R\mathcal{#1}\poly\big)}\newcommand{\cy}[1]{\mathbb{H}^\bullet_{\operatorname{CE}}(A,\mathcal{#1}\poly)}$Kontsevich's formality the…

Survey and benchmark high-dimensional Bayesian optimization of discrete sequences.

New algorithm learns random neural networks efficiently.

Triangle Artin groups split as graphs of free groups under specific conditions.

The paper defines and analyzes configuration Lie groupoids and orbifold braid groups.

In this paper, we obtain a sharp upper bound for the sum of the first $k$-th eigenvalues for this Dirichlet problem of poly-Laplacian with any order, which is viewed as an extension of the result due to Cheng and Wei (Journal of Differential Equations, 255 (2013), 220-233). In particular, if $l=2$ and $k$ is large enou…

In this text we give a decomposition result on polynomial poly-vector fields generalizing a result on the decomposition of homogeneous Poisson structures. We discuss consequences of this decomposition result in particular for low dimensions and low degrees. We provide the tools to calculate simple cubic Poisson structu…

New algorithms solve linear algebra problems in sublinear time.

Let $f:\mathbb{S}^{d-1}\times \mathbb{S}^{d-1}\to\mathbb{S}$ be a function of the form $f(\mathbf{x},\mathbf{x}') = g(\langle\mathbf{x},\mathbf{x}'\rangle)$ for $g:[-1,1]\to \mathbb{R}$. We give a simple proof that shows that poly-size depth two neural networks with (exponentially) bounded weights cannot approximate $f…

Polystable bundles on Kaehler manifolds are stable if their classes are stable.

Proves connection between $\ell^2$-Betti numbers and BNSR invariants.

Study bandit problems with BMO functions, achieving poly-log $δ$-regret.

Many problems in computer vision and recommender systems involve low-rank matrices. In this work, we study the problem of finding the maximum entry of a stochastic low-rank matrix from sequential observations. At each step, a learning agent chooses pairs of row and column arms, and receives the noisy product of their l…

Estimates linear models from self-selected data, addressing econometric challenges.

The Farrell-Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example for discrete subgroups of Lie groups, virtually poly-infinite cyclic groups, Artin braid groups, a class of virtually poly-surface groups and virtually solvable lin…

Proves graph 3-manifold groups have two specific properties.

Optimized GAN discriminator using polyharmonic interpolation.

We prove local polyhomogeneity of asymptotically real or complex hyperbolic Einstein metrics, with application to unique continuation problems.

New algebraic framework for Jacobi manifolds connects geometric mechanics and dimensional analysis.

This article has two purposes. In \cite{R3} (math.KT/0405211) we showed that the FIC (Fibered Isomorphism Conjecture for pseudoisotopy functor) for a particular class of 3-manifolds (we denoted this class by \cal C) is the key to prove the FIC for 3-manifold groups in general. And we proved the FIC for the fundamental …

In this paper, we show that along $\mathbb Q$-Fano fibration, when general fibres, base and central fiber (with at worst Kawamata log terminal singularities)are K-poly stable then there exists a relative Kähler-Einstein metric. We introduce the fiberwise Kähler-Einstein foliation and we mention that the main difficulty…

New polystability theory connects Calabi-Yau varieties to gravitational instantons.

New algorithm reduces runtime for robust sparse mean estimation.

Simpler algorithm learns shallow networks faster.

Polynomial-time algorithm for estimating covariance in corrupted Gaussian data.

In this note we point out an error in the above paper and refer to some papers where this error is corrected and a more general theorem is proved.