Solves smoothing problem in Chow's connectivity theorem.
problem Smoothing problem in Chow's connectivity theorem.
method Solution provided.
result Solves the smoothing problem in Chow's theorem.
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
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48 results for “smooth problems”
Smooth even solutions found for a generalized convex geometry problem.
problem Dual Orlicz-Minkowski problem in convex geometry.
method Geometric flow involving Gauss curvature and normal vectors.
result Existence of smooth even solutions for smooth even measures.
Smooth Schrödinger Bridges improve trajectory inference by smoothing Gaussian processes.
problem Improving trajectory inference in applications like particle tracking.
method Generalizes Schrödinger Bridge problem to smooth Gaussian processes, solving the problem on phase space.
result The method outperforms existing methods on real datasets.
Prescribed curvature problemmath.AP
Paper finds smooth convex solutions to curvature problem.
problem Finding smooth, convex solutions to curvature problems.
method Established existence of solutions through mathematical analysis.
result Smooth, origin-symmetric, strictly convex solutions found.
The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to generalize the concept of Lipschitz smoothness condition to the relative smoothn…
In this paper, we develop a novel {\bf ho}moto{\bf p}y {\bf s}moothing (HOPS) algorithm for solving a family of non-smooth problems that is composed of a non-smooth term with an explicit max-structure and a smooth term or a simple non-smooth term whose proximal mapping is easy to compute. The best known iteration compl…
Paper improves stochastic bilevel optimization methods for highly-smooth problems.
problem Finding -stationary points in stochastic bilevel optimization.
method Proposes FSA- methods using th-order finite differences for hyper-gradient approximation.
result Achieves upper complexity bound of for th-order smooth problems.
We consider the problem of defining the structure of a smooth manifold on the various spaces of piecewise-smooth loops in a smooth finite dimensional manifold. We succeed for a particular type of piecewise-smooth loops. We also examine the action of the diffeomorphism group of the circle. It is not a useful action on t…
Proves existence of smooth metrics with specific curvature properties.
problem Existence of smooth metrics with prescribed negative Ricci curvature.
method Formulated and proved for general domains in Euclidean space.
result Existence of smooth complete conformal metrics with prescribed negative Ricci curvature.
We study a non-parametric multi-armed bandit problem with stochastic covariates, where a key complexity driver is the smoothness of payoff functions with respect to covariates. Previous studies have focused on deriving minimax-optimal algorithms in cases where it is a priori known how smooth the payoff functions are. I…
The Rectangular Peg Problemmath.GT
Rectangles can fit on smooth curves, proving a theorem about Klein bottles.
problem Fitting rectangles on smooth curves.
method Shevchishin's theorem about Klein bottle embeddings.
result Similar rectangles can be placed on smooth Jordan curves.
In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if admissible controls satisfy an integrability condition or if it is contin…
We provide improved convergence rates for various \emph{non-smooth} optimization problems via higher-order accelerated methods. In the case of regression, we achieves an iteration complexity, breaking the barrier so far present for previous methods. We arrive at a similar rate fo…
Smooth solutions found for a specific type of Yamabe problem.
problem Regularity of viscosity solutions to the -Yamabe problem in the negative cone.
method Analysis of Lipschitz viscosity solutions with specific assumptions.
result Existence and smoothness of solutions away from a negligible set.
Sparse Polyak improves high-dimensional statistical estimation.
problem High-dimensional statistical estimation problems with growing problem dimension.
method Sparse Polyak modifies Polyak's adaptive step size to estimate restricted Lipschitz smoothness.
result Sparse Polyak achieves optimal statistical precision with fewer iterations.
This work speeds up hyperparameter selection for non-smooth convex models using implicit differentiation.
problem Optimizing hyperparameters of non-smooth convex models.
method Implicit differentiation of proximal gradient and coordinate descent methods.
result Implicit differentiation can speed up hyperparameter optimization, especially for non-smooth problems.
Label smoothing improves model performance even with noisy labels.
problem Mitigating label noise in deep learning models.
method Examined label smoothing as a technique to cope with label noise and compared it to loss-correction methods.
result Label smoothing is competitive with loss-correction techniques under label noise and beneficial for distillation from noisy data.
New algorithm tackles nonconvex machine learning problems with adaptive normalization and independent sampling.
problem Nonconvex machine learning problems with generalized-smoothness.
method Adaptive gradient normalization, independent sampling, and gradient clipping.
result Achieves an O(ε^(-4)) sample complexity for fast convergence.
We prove that any isometry between the unit spheres of -smooth (more generally, absolutely smooth) smooth Banach spaces extends to a linear isometry of the Banach spaces. This answers the famous Tingley's problem in the class of absolutely smooth -dimensional Banach spaces.
Unified flow solves Christoffel-Minkowski problem for .
problem Solving the Christoffel-Minkowski problem for .
method Anisotropic expanding flow of smooth hypersurfaces with speed .
result The flow converges to a solution of the Christoffel-Minkowski problem.
Research on the least complex surface in certain 4D shapes.
problem Finding the simplest surface in specific four-dimensional shapes.
method Analyzing smooth four-manifolds to determine minimal genus.
result Results on the minimal genus for studied four-manifolds.
Smooth solutions found for a curvature problem in hyperbolic space.
problem Existence of smooth complete hypersurfaces with prescribed curvature in hyperbolic space.
method Utilized Pogorelov type interior second order estimate.
result Affirmative answers for specific curvature cases in hyperbolic space.
Develops PRPCA for smooth image recovery combining low-rank and smoothness.
problem Image matrix recovery under low-rank and smoothness assumptions.
method Projected Robust PCA (PRPCA) framework combining low-rank and smoothness.
result Explicit statistical guarantees for PRPCA, reducing matrix dimensionality.
Optimization viewpoint on Kalman smoothing, with applications to robust and sparse estimationmath.OC
In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least squares problem, highlight special structure, and show that the classic filtering an…
Obstructions to special Lagrangian desingularizations and the Lagrangian prescribed boundary problemmath.DG
We exhibit infinitely many, explicit special Lagrangian isolated singularities that admit no asymptotically conical special Lagrangian smoothings. The existence/ nonexistence of such smoothings is an important component of the current efforts to understand which singular special Lagrangians arise as limits of smooth sp…
In this article, we introduce an analogous problem to Yamabe type problem considered by Case, J., which generalizes the Escobar-Riemann mapping problem for smooth metric measure spaces with boundary. The last problem will be called Escobar-Riemann mapping type problem. For this purpose, we consider the generalization o…
Advances smooth over-parameterization for solving non-smooth optimization problems.
problem Non-smooth optimization with structural constraints in imaging and machine learning.
method Smooth over-parameterization of non-smooth problems, using gradient descent and mirror descent.
result Gradient descent on the reformulated smooth problem converges efficiently without parameter tuning.
Study bandit problem on smooth graph functions for recommender systems.
problem Online learning problems involving graphs, like content-based recommendation.
method Introduced spectral bandit problem and two algorithms that scale linearly in effective dimension.
result Learned user preferences for thousands of items from just tens nodes evaluations.
tl;dr: no, it cannot, at least not on average on the standard archive problems. We assess whether using six smoothing algorithms (moving average, exponential smoothing, Gaussian filter, Savitzky-Golay filter, Fourier approximation and a recursive median sieve) could be automatically applied to time series classificatio…
A mass-type invariant for smooth metric measure spaces and its relation with the fractional Yamabe problem
problem Defining and analyzing a mass-type invariant for smooth metric measure spaces
method Defining a mass-type quantity and showing its geometric invariance properties
result The mass-type quantity has a close relation with the fractional Yamabe problem and the relevant Green's function
Stochastic approximation proves asymptotic normality for non-smooth problems.
problem Solving non-smooth stochastic approximation problems.
method Stochastic approximation algorithms for solving smooth equations, extended to non-smooth problems.
result Asymptotic normality and optimality in non-smooth stochastic approximation is proven.
New algorithm solves federated minimax optimization problems.
problem Federated minimax optimization challenges.
method Federated Stochastic Smoothed Gradient Descent Ascent (FESS-GDA).
result FESS-GDA uniformly solves federated minimax problems.
We prove that compact Cauchy horizons in a smooth spacetime satisfying the null energy condition are smooth. As an application, we consider the problem of determining when a cobordism admits Lorentzian metrics with certain properties. In particular, we prove a result originally due to Tipler without the smoothness hypo…
Variational problems that involve Wasserstein distances have been recently proposed to summarize and learn from probability measures. Despite being conceptually simple, such problems are computationally challenging because they involve minimizing over quantities (Wasserstein distances) that are themselves hard to compu…
By means of a general gluing and conformal-deformation construction, we prove that any smooth, metrically complete Riemannian manifold with smooth boundary can be realized as a closed domain into a smooth, geodesically complete Riemannan manifold without boundary. Applications to Sobolev spaces, Nash embedding and loca…
Study on special Lagrangian curvature potential equation, proving existence and uniqueness of smooth solutions.
problem Second boundary value problem for special Lagrangian curvature potential equation.
method Method of continuity with a-priori estimate.
result Existence and uniqueness of smooth uniformly convex solutions.
Input-dependent smoothing mitigates classical issues but suffers from the curse of dimensionality.
problem Certifiably robust classifiers with input-dependent smoothing suffer from the curse of dimensionality.
method Proposed a theoretical and practical framework for input-dependent smoothing under strict restrictions.
result Input-dependent smoothing mitigates some classical issues but is limited by the curse of dimensionality.
The Kazdan-Warner problem is solved for Riemann surfaces with smooth boundaries.
problem Realizing smooth functions as Gaussian and geodesic curvatures on compact Riemann surfaces.
method Existence results of Brezis-Merle type equations and uniformization theorem extension.
result Any smooth function on compact Riemann surface with smooth boundary can be realized as a Gaussian curvature function and any on the boundary as a geodesic curvature function.
New approach to solving minimal surface system Dirichlet problem on smooth domains.
problem Solving Dirichlet problem for minimal surface system on smooth domains.
method Using mean curvature flow (MCF) with boundary conditions and non-negative Ricci curvature assumption.
result Existence of long-time mean curvature flow and existence result for exterior Dirichlet problem.
The paper tackles a bandit problem on graphs with smooth functions, aiming to recommend items with high expected ratings.
problem Online learning problems involving graphs, such as content-based recommendation.
method Introduced the notion of effective dimension and proposed two algorithms for solving the problem.
result The algorithms can learn good estimators of user preferences from just tens of nodes evaluations.
Smooth solutions found for hydrodynamic equations.
problem Geodesic equations on diffeomorphism groups.
method Proving smoothness of solutions and constructing exponential maps.
result Smooth solutions match boundary conditions.
This paper considers a time-inconsistent stopping problem in which the inconsistency arises from non-constant time preference rates. We show that the smooth pasting principle, the main approach that has been used to construct explicit solutions for conventional time-consistent optimal stopping problems, may fail under …
We prove the existence of a local smooth Levi decomposition for smooth Poisson structures and Lie algebroids near a singular point. In the appendix of this paper, we show an abstract Nash-Moser normal form theorem, which generalizes our Levi decomposition result and which may be helpful in the study of other smooth nor…
AdaGrad fails to adapt to Hölder-smoothness in composite optimization problems.
problem AdaGrad's convergence rate is suboptimal for composite objectives.
method Exhibited a simple one-dimensional convex problem to highlight AdaGrad's limitations.
result AdaGrad does not achieve the classical convergence rate for Hölder-smooth objectives.
Study on spectral asymptotics in elasticity on smooth manifolds.
problem Analyzing spectral asymptotics in linear elasticity on smooth manifolds.
method Established two-term spectral asymptotics for boundary value problems in linear elasticity.
result Corrected erroneous results in previous studies.
Paper finds lower bounds for eigenvalues of Bi-drifted Laplacian on smooth metric measure spaces.
problem Eigenvalue problems for Bi-drifted Laplacian on compact manifolds with boundary conditions.
method Obtained lower bounds using specific curvature conditions.
result Lower bounds for the first eigenvalue of Bi-drifted Laplacian.
The paper proves estimates for solutions to nonlinear equations on manifolds with boundary.
problem Boundary estimates for fully nonlinear Yamabe equations on Riemannian manifolds.
method Deriving a priori second derivative estimates for subsolutions.
result Existence of smooth solutions with uniform estimates.
Smooths out complex shapes into simpler forms.
problem Transforming complex shapes into simpler, smooth forms.
method Perturbing minimizing hypercones and viscosity mean convex cones into smooth, properly embedded hypersurfaces.
result Properly embedded smooth minimizing hypersurfaces and self-expanders are achieved.