arXiv research

The paper analyzes the performance of empirical risk minimization for $p$-norm linear regression.

In this paper we study the area minimizing problem in some kinds of conformal cones. This concept is a generalization of the cones in Eulcidean spaces and the cylinders in product manifolds. We define a non-closed-minimal (NCM) condition for bounded domains. Under this assumption and other necessary conditions we estab…

Characterizes concept classes for optimistic online learning.

Extends global stability of Minkowski spacetime to minimal decay assumptions.

Formula proves monotonicity for anisotropic minimal hypersurfaces.

It is shown that $m$ disjoint sets with fixed Gaussian volumes that partition $\mathbb{R}^{n}$ with minimum Gaussian surface area must be $(m-1)$-dimensional. This follows from a second variation argument using infinitesimal translations. The special case $m=3$ proves the Double Bubble problem for the Gaussian measure,…

Extends Minkowski stability proof to minimal decay assumptions.

GALA framework learns invariant graph representations via environment augmentation with minimal assumptions.

Paper finds conditions for minimal hypersurfaces in S^6 with constant scalar curvature.

Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted to validate the model and to determine whether the regression assumptions are me…

In this paper, under the assumption of Gauss curvature vanishing at infinity, we will prove Meeks' conjecture: the number of disjointly supported minimal graphs in $\mathbb{R}^3$ is at most two.

Improved median of means estimator with tighter bounds.

Study minimal volume entropy for free-by-cyclic groups and 2D right-angled Artin groups.

Paper achieves $ε^{-2}$ sample complexity for actor-critic methods with minimal assumptions.

We study the asymptotic Dirichlet problem for $f$-minimal graphs in Cartan-Hadamard manifolds $M$. $f$-minimal hypersurfaces are natural generalizations of self-shrinkers which play a crucial role in the study of mean curvature flow. In the first part of this paper, we prove the existence of $f$-minimal graphs with pre…

Study reward-free RL in non-linear settings, improving efficiency and removing assumptions.

The paper analyzes risk bounds and Rademacher complexity in batch RL.

We study the existence of a minimal supersolution for backward stochastic differential equations when the terminal data can take the value +$\infty$ with positive probability. We deal with equations on a general filtered probability space and with generators satisfying a general monotonicity assumption. With this minim…

We study the pricing and hedging of derivatives in incomplete financial markets by considering the local risk-minimization method in the context of the benchmark approach, which will be called benchmarked local risk-minimization. We show that the proposed benchmarked local risk-minimization allows to handle under extre…

Sharp stability in Almgren problem solved in any dimension.

The Besson-Courtois-Gallot theorem is proven for noncompact finite volume Riemannian manifolds. In particular, no bounded geometry assumptions are made. This proves the minimal entropy conjecture for nonuniform rank one lattices.

Minimal surfaces in lens spaces identified with specific counts.

The study examines conditions for minimal volume entropy of simplicial complexes.

Dirac-harmonic maps are uncoupled under certain conditions.

The sparse representation classifier (SRC) has been utilized in various classification problems, which makes use of L1 minimization and works well for image recognition satisfying a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence to the original SRC und…

The paper proves an infinite double bubble theorem in higher dimensions.

Direct method finds Yang-Mills connections for SO(3) bundles.

Paper shows faster convergence to local-minimizers in over-parametrized models under interpolation-like conditions.

Analytic proof for minimal rank Sard conjecture.

We give a partial local description of minimal hypersurfaces $M^3$ with identically zero Gauß-Kronecker curvature function in the unit 4-sphere $\Bbb{S}^4(1)$, without assumption on the compactness of $M^3$.

Paper shows robust generative learning with minimal assumptions on target distributions.

Let N be a complete, homogeneously regular Riemannian manifold of dimension greater than 2 and let M be a compact submanifold of N. Let $Σ$ be a compact orientable surface with boundary. We show that for any continuous $f: (Σ, \partial Σ) \rightarrow (N, M)$ for which the induced homomorphism on certain fundamental gro…

New algorithm reduces regret in combinatorial causal bandits without graph structure.

New method uses minimal assumptions for machine learning, improving performance and speed.

Paper simplifies balancing weights by relaxing outcome assumptions.

We show that strictly stable components of Allen-Cahn minimal hypersurfaces always occur with multiplicity one. We also establish the uniqueness of solutions converging to nondegenerate hypersurfaces with multiplicity one. Our results work in all dimensions and without variational assumptions on the Allen-Cahn solution…

We consider two natural classes of minimal laminations in three-manifolds. Both classes may be thought of as limits - in different senses - of embedded minimal disks. In both cases, we prove that, under a natural geometric assumption on the three-manifold, the leaves of these laminations are topologically either disks,…

Let $(M, g)$ be an $n$-dimensional complete Riemannian manifold with $Ric(M)\geq-(n-1)Q$, where $Q\geq0$ is a constant. We obtain an interior gradient bound for minimal graphs in $M\times R$ under some technical assumptions. For details, see Theorem 2.

New theorem on 3-manifolds with curvature and convex boundary.

New method speeds up diffusion models without requiring complex assumptions.

We show that in the setting of proper metric spaces one obtains a solution of the classical two-dimensional Plateau problem by minimizing the energy, as in the classical case, once a definition of area (in the sense of convex geometry) has been chosen appropriately. We prove the quasi-convexity of this new definition o…

In this paper, we prove the nonexistence of $L^2$ harmonic 1-forms on a complete super stable minimal submanifold $M$ in hyperbolic space under the assumption that the first eigenvalue $λ_1 (M)$ for the Laplace operator on $M$ is bounded below by $(2n-1)(n-1)$. Moreover, we provide sufficient conditions for minimal sub…

The study finds conditions for area-minimizing cones over submanifolds.

Unified framework for best arm identification and dueling bandits regret minimization.

Clusters on simple manifolds have connected boundaries.

The paper studies stability and minimizing properties of higher codimensional surfaces in Euclidean space.

Unified review of Conformal Prediction theory and applications.

Improved analysis for diffusion models reduces KL divergence error dependence on data dimension and discretization step size.