We establish continuous maximal regularity results for parabolic differential operators acting on sections of tensor bundles on Riemannian manifolds. As an application, we show that solutions to the Yamabe flow instantaneously regularize and become real analytic in space and time. The regularity result is obtained by i…
On-device research index
arXiv research
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.
168,742 papers · 148 categories
Trend · papers per month
48 results for “regularity results”
LLE produces unwanted results without regularization, which can be prevented with regularization.
problem LLE's inherent unwanted results without regularization.
method Mathematical proof and numerical examples of regularization effectiveness.
result Regularization prevents unwanted results in LLE.
The paper studies convergence rates of Tsallis entropic regularization in optimal transport.
problem Optimal transport with regularization.
method Γ-convergence and quantization/shadow arguments.
result Derives convergence rate of Tsallis entropic regularization.
Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect. Although connection between Wasserstein DRO and regularization has been established in several settings, existin…
Uniform small energy regularity for fractional geometric problems proved.
problem Proving regularity for fractional geometric problems.
method Analyzing parabolic boundary reaction Ginzburg-Landau problems and fractional harmonic maps to spheres.
result Uniform small energy regularity results for , answering a posed question.
Optimal Rates of Sketched-regularized Algorithms for Least-Squares Regression over Hilbert Spacesstat.ML
We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect to variants of norms, under a capacity assumption on the hypothesis space and a …
Regularized policies are robust to adversarial rewards.
problem Understanding the effects of regularization on policy exploration and robustness.
method Using Fenchel duality to derive the dual problem of the regularized RL objective, showing the optimal policy is robust to adversarial rewards.
result Regularized policies are optimal for a reinforcement learning problem under adversarial reward conditions.
New iterative regularization method tackles non-smooth, non-strongly convex functionals.
problem Tackles non-smooth, non-strongly convex functionals in regularization problems.
method Primal-dual algorithm with convergence and stability analysis.
result First iterative regularization procedure for non-smooth, non-strongly convex functionals.
Study examines stability of image-reconstruction algorithms using variational regularization.
problem Stability and robustness of image-reconstruction algorithms in medical imaging.
method Review and novel stability results for -regularized linear inverse problems, focusing on .
result Guarantees Lipschitz continuity for small and Hölder continuity for larger in function spaces.
Regularity results for geodesic X-ray transform on nonsmooth manifolds
problem Geodesic X-ray transform on nonsmooth simple manifolds
method Symbol smoothing arguments and pseudodifferential operators with low regularity symbols
result Improved injectivity results for functions
We obtain the $C^{\a}$ regularity for weak solutions of a class of non-homogeneous ultraparabolic equation, with measurable coefficients. The result generalizes our recent $C^{\a}$ regularity results of homogeneous ultraparabolic equation.
The use of convex regularizers allows for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones. However, the resultant optimization problem is much harder. In this paper, for a …
In this paper, we present a probability one convergence proof, under suitable conditions, of a certain class of actor-critic algorithms for finding approximate solutions to entropy-regularized MDPs using the machinery of stochastic approximation. To obtain this overall result, we prove the convergence of policy evaluat…
A fast sketching algorithm solves regularized least squares problems efficiently.
problem Solving large-scale optimization problems with convex or nonconvex regularization.
method Sketching for Regularized Optimization (SRO) algorithm that generates a sketch of the original data matrix and solves the sketched problem.
result General theoretical results for the approximation error between the original and sketched problems, including minimax rates for sparse signal estimation.
Optimizes biharmonic map regularity using stratification methods.
problem Improving the known almost optimal regularity of biharmonic maps.
method Quantitative stratification method.
result Optimal regularity results for minimizing biharmonic maps.
In this paper we consider existence and multiplicity results concerning affine connections on -manifolds whose coefficients are as regular as one needs, following the regularity theory introduced in arXiv:1908.04442. We show that if admits a -structure, then the existence of such regular con…
The study connects group structure to smooth actions on one-manifolds.
problem Understanding how group actions affect the smoothness of manifolds.
method Analyzes the relationship between group algebraic structure and smoothness of group actions on one-dimensional manifolds.
result Uniform construction of groups acting on compact interval and circle with prescribed regularity.
We prove regularity results up to the boundary for time independent generalized Maxwell equations on Riemannian manifolds with boundary using the calculus of alternating differential forms. We discuss homogeneous and inhomogeneous boundary data and show 'polynomially weighted' regularity in exterior domains as well.
Weight decay is one of the standard tricks in the neural network toolbox, but the reasons for its regularization effect are poorly understood, and recent results have cast doubt on the traditional interpretation in terms of regularization. Literal weight decay has been shown to outperform regularization for…
Paper explores how DPP sampling can implicitly regularize kernel regression.
problem Improving kernel regression by reducing redundancy in data.
method Using Determinantal Point Processes (DPPs) to sample subsets implicitly regularizes ridgeless Kernel Regression.
result Ensemble of ridgeless regressors can be effective for datasets with redundant information.
Multiparameter regularization and aggregation in the context of polynomial functional regressionstat.ML
Study introduces a new method for multiple parameter regularization in polynomial functional regression.
problem Handling varying regularization parameters in polynomial functional regression.
method Developed a theoretically grounded algorithm for multiple parameter regularization and model aggregation.
result Promising results from evaluations on synthetic and real-world data.
Optimal Regularization Under Uncertainty: Distributional Robustness and Convexity Constraintsmath.OC
New framework for robust regularization under uncertain data distributions.
problem Addressing ill-posed inverse problems and statistical estimation under distributional uncertainty.
method Distributionally robust optimal regularization using convex duality.
result Identifies robust regularizers that remain effective under data distributional perturbations.
Paper analyzes Nyström regularization for time series forecasting with sequential sub-sampling.
problem Learning rate analysis of Nyström regularization for -mixing time series.
method Banach-valued Bernstein inequality and integral operator approach for -mixing sequences.
result Almost optimal learning rates for Nyström regularization with sequential sub-sampling.
Improved optimal regularity for harmonic almost complex structures.
problem Establishing optimal regularity for harmonic almost complex structures.
method Quantitative stratification method and rectifiability of singular strata.
result Optimal regularity theory for energy minimizing harmonic almost complex structures.
Improved MMD test for non-Euclidean data with spectral regularization.
problem Inefficient and impractical MMD goodness-of-fit tests for non-Euclidean data.
method Spectral regularization of MMD test, extending results to general cases.
result Minimax optimal test for non-Euclidean data with appropriate regularization.
Study iterative regularization for linear models with convex bias, improving robust sparse recovery.
problem Improving robust sparse recovery with iterative regularization for linear models.
method Primal-dual gradient approach, analyzing convergence in presence of noise, combining regularization and optimization.
result Theoretical results show state-of-the-art performances with computational speed-ups.
This paper explores how entropic regularization improves Wasserstein estimators' performance.
problem Improving the approximation and estimation properties of Wasserstein estimators.
method Entropic regularization of optimal transport costs to smooth Wasserstein estimators.
result Entropic regularization can achieve comparable statistical performance to un-regularized estimators at lower computational cost.
This work explores Target Networks and Functional Regularization in deep Reinforcement Learning.
problem Stability and performance issues in deep Reinforcement Learning due to target value instability.
method Proposes and studies an explicit Functional Regularization approach as a replacement for Target Networks.
result Functional Regularization improves performance and stability compared to Target Networks.
Proves regularity of isomorphisms between hyperbolic 3-manifolds.
problem Understanding the regularity of isomorphisms between hyperbolic 3-manifolds.
method Strengthened a previous result by proving regularity in the sense of Boileau and Friedl.
result Profinite isomorphisms of hyperbolic 3-manifolds are regular.
Deep networks adapt to function regularity and data distribution.
problem Understanding deep learning's adaptability to function regularity and data distribution.
method Developed nonparametric approximation and estimation theories for a broad class of functions using deep ReLU networks.
result Deep neural networks are adaptive to different regularity of functions and nonuniform data distributions.
We establish an optimal regularity result for parametrized two-dimensional stationary varifolds. Namely, we show that the parametrization map is a smooth minimal branched immersion and that the multiplicity function is constant. We provide some applications of this regularity result, especially in the calculus of varia…
We extend the validity of the Penrose singularity theorem to spacetime metrics of regularity . The proof is based on regularisation techniques, combined with recent results in low regularity causality theory.
This paper uses the relationship between graph conductance and spectral clustering to study (i) the failures of spectral clustering and (ii) the benefits of regularization. The explanation is simple. Sparse and stochastic graphs create a lot of small trees that are connected to the core of the graph by only one edge. G…
We establish regularity results for critical points to energies of immersed surfaces depending on the first and the second fundamental form exclusively. These results hold for a large class of intrinsic elliptic Lagrangians which are sub-critical or critical. They are derived using uniform regularity estimates whic…
New method for training deep neural networks with regularization, converging to better generalization.
problem Improving generalization of deep neural networks through explicit regularization.
method Regularizer Mirror Descent (RMD) method, inspired by convergence properties of stochastic mirror descent (SMD).
result RMD converges to a point close to the minimizer of the cost function, leading to better generalization performance.
New approach connects reinforcement learning robustness and regularization.
problem Dealing with external uncertainty in reinforcement learning.
method Introducing Wasserstein distributionally robust MDPs and a new regularizer.
result Established a dual relation between robust MDPs and regularization.
Regularization plays an important role in generalization of deep neural networks, which are often prone to overfitting with their numerous parameters. L1 and L2 regularizers are common regularization tools in machine learning with their simplicity and effectiveness. However, we observe that imposing strong L1 or L2 reg…
New theorem for generalized group sparsity improves consistency and convergence rates.
problem Improving statistical inference in high-dimensional data with element-wise and group-wise sparsity.
method Developed a generalized version of Sparse-Group Lasso and proved a universal theorem for consistency and convergence rates.
result Obtained results on consistency and convergence rates for different forms of double sparsity regularization.
Extends Campanato theory to multi-valued functions for geometric variational problems.
problem Regularity of multi-valued functions in geometric variational problems.
method Adapting Campanato's ideas to multi-valued functions, proving regularity theorems.
result Established regularity for multi-valued harmonic functions and stationary integral varifolds.
On the Optimal Regularity Implied by the Assumptions of Geometry II: Connections on Vector Bundlesmath.DG
Extends optimal regularity and compactness to vector bundles over non-Riemannian manifolds.
problem Optimal regularity and compactness for connections on vector bundles.
method Derive RT-equations, establish existence theory, handle curvature up to .
result Optimal regularity and compactness extended to vector bundles over non-Riemannian manifolds.
Paper studies heat flow for maps on manifolds, avoiding singularities.
problem Avoiding singularities in heat flow for maps on manifolds.
method Introduces regularized conformal heat flow for -harmonic maps.
result Regularized -conformal heat flow does not develop finite time singularities.
Proves regularity of harmonic maps into Teichmüller space.
problem Harmonic maps into Teichmüller space and their singularities.
method Analyzes harmonic maps from Riemannian domains to Teichmüller space with specific conditions.
result If a harmonic map intersects a stratum, it is entirely contained in that stratum.
Linear Convergence of Entropy-Regularized Natural Policy Gradient with Linear Function Approximationcs.LG
Entropy-regularized NPG converges linearly with linear function approximation.
problem Analyzing convergence of entropy-regularized NPG with function approximation.
method Established finite-time convergence analyses with entropy regularization and linear function approximation.
result Entropy-regularized NPG achieves linear convergence up to a function approximation error.
We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably dominates its conventional counterpart in terms of mean square deviations. We es…
Improved Kriging model reduces prediction errors.
problem Improving prediction accuracy in Kriging models.
method Theta-regularized Kriging model with Lasso, Ridge, and Elastic-net penalties.
result The Theta-regularized Kriging model outperforms other penalized Kriging models in accuracy and stability.
Regularity and stability results for the level set flow via the mean curvature flow with surgerymath.DG
In this article we use the mean curvature flow with surgery to derive regularity estimates for the level set flow going past Brakke regularity in certain special conditions allowing for 2-convex regions of high density. We also show a stability result for the plane under the level set flow.
The paper shows how data augmentation and regularization can enforce group equivariance in machine learning models.
problem Improving model performance by leveraging known symmetries in machine learning tasks.
method Training with data augmentation and regularization to enforce group equivariance.
result Equivariance of the trained model can be achieved through training on augmented data in tandem with regularization.
Bayesian regularization improves policy performance in noisy MDPs.
problem Suboptimal policies from estimated model parameters.
method Bayesian regularization of MDP objective function with prior information.
result Regularized policies show better robustness against model noise.