Developed a method to compute the cost of sphere eversion using Willmore energies.
problem Computing the cost of sphere eversion in 3D Euclidean space.
method Minmax procedure for constructing Willmore surfaces and applying it to sphere eversion.
result Computed the cost of sphere eversion in terms of Willmore energies.
Study MinMax methods for optimization problems, including optimal transport.
problem Optimization problems, especially optimal transport.
method MinMax framework, regularization, neural networks, approximation theorems.
result Justification of neural networks for solving optimization problems.
New method generates critical points for complex functionals.
problem Proving the Willmore conjecture in complex geometric settings.
method Minmax hierarchies and fibrations for critical points.
result New proof of the Willmore conjecture.
A new algorithm improves GAN training stability and performance.
problem Training GANs is difficult due to variance and rotational dynamics.
method Proposes Lookahead-Minmax algorithm for minmax optimization.
result Significant improvement in GAN performance and stability.
In this paper, we will study the existence problem of minmax minimal torus. We use classical conformal invariant geometric variational methods. We prove a theorem about the existence of minmax minimal torus in Theorem 5.1. Firstly we prove a strong uniformization result(Proposition 3.1) using method of [1]. Then we use…
Generates critical points in manifolds for higher index min-max problems.
problem Finding critical points in Banach manifolds with Finsler structures.
method Minmax hierarchy and viscosity approach to minimal surfaces.
result Characterization of minimal surfaces in S3 and conjecture for next surfaces. The paper evaluates contingent claim prices using trajectory-based models without probabilistic assumptions.
problem Evaluating contingent claim prices in markets without probabilistic or topological assumptions.
method Develops a backward recursive method and dynamic programming to evaluate minmax bounds.
result Defines a global minmax optimization problem as a local one, reducing complexity.
New algorithms for ranking data under two distance measures.
problem Rank aggregation under Kendall τ and Spearman footrule distances.
method Constant-approximation algorithms for NP-hard problems.
result Illustrative applications on the Mallows model and genomic data.
Proves existence of a single-valued minimal hypersurface in compact manifolds.
problem Existence of multiplicity-1 minimal hypersurfaces in compact Riemannian manifolds.
method Modified minmax construction with Allen-Cahn approximation and valley point optimization.
result Existence of a smooth, closed minimal hypersurface with multiplicity 1 in bumpy metrics.
Study examines the scenario approach for robust optimization, focusing on nonconvex cases.
problem Robust optimization with nonconvex uncertainty sets.
method Scenario approach via i.i.d sampling, analysis of concentration of measures, asymptotic and finite sample guarantees.
result Obstruction to consistency in noncompact decision sets, finite sample guarantees for nonconvex problems.
Estimates conditional mutual information using a minmax formulation.
problem Estimating conditional mutual information in high dimensions.
method Uses a minmax optimization problem to train a neural network.
result Improves estimation accuracy compared to existing methods.
New proof of minimal hypersurface existence in manifolds with positive Ricci curvature.
problem Existence of minimal hypersurfaces in manifolds with positive Ricci curvature.
method One-parameter minmax construction via Allen--Cahn energy.
result Existence of a multiplicity-1 closed minimal hypersurface.
The study finds a continuous map achieving minmax area under Legendrian constraints.
problem Finding minmax areas under Legendrian constraints in 5D Sasakian manifolds.
method Continuous conformal Legendrian map with bounded multiplicity satisfying a weak Hamiltonian Minimal Equation.
result Continuous map achieving minmax area with bounded multiplicity.
Introduces self-regularization for analyzing learning algorithms.
problem Analyzing and optimizing learning algorithms without explicit regularization.
method Develops a self-regularization framework for learning algorithms.
result Provides statistical analysis and minmax-optimal rates for self-regularized algorithms.
Gradient descent-ascent converges to strict local minmax equilibria with a finite timescale separation.
problem Analyzing the convergence of gradient descent-ascent in non-convex, non-concave games with a finite timescale separation.
method Investigates the role of a finite timescale separation parameter τ on gradient descent-ascent in two-player zero-sum games, providing convergence rates and non-convergence results.
result Gradient descent-ascent converges to strict local minmax equilibria for a finite timescale separation parameter τ*.
The study improves model selection by considering curvature in statistical manifolds.
problem Model selection and avoiding overfitting in statistical manifolds.
method Assuming a smooth manifold, using Riemannian geometry tools, and deriving minmax regret.
result Deriving a sharper expression for minmax regret in statistical manifolds.
Study on optimal rates for sequential probability assignment using smoothed analysis.
problem Optimal rates for sequential probability assignment under smoothed adversaries.
method General-purpose reduction from minimax rates to transductive learning, development of an efficient algorithm using MLE oracle.
result Optimal (logarithmic) fast rates for parametric and finite VC dimension classes, sublinear regret for general classes.
ADMM algorithm solves nonlinear matrix decompositions efficiently.
problem Nonlinear matrix decompositions for various applications.
method Alternating Direction Method of Multipliers (ADMM) for nonlinear matrix factorization.
result The method efficiently solves diverse nonlinear matrix decompositions.
New method finds best arm minimizing mean-squared error in correlated bandits.
problem Finding an arm that best captures information about other arms.
method Formulated correlated bandit problem, derived MSE estimator, proposed algorithm.
result Proposed algorithm identifies best arm with error probability bounds.
Paper finds significant phase shifts between financial underlyings.
problem Identifying lead-lag relationships between financial markets.
method Computing phase shifts of local extrema on unit circle.
result Strong correlations and phase shifts observed in financial markets.
Establishes regularity of conformal harmonic maps.
problem Ensuring smoothness of harmonic maps.
method Viscosity techniques for stationary varifolds.
result Weakly conformal maps are smooth if stationary.
Bayesian adversaries can outsmart traditional adversarial attacks.
problem Bayesian adversaries can manipulate machine learning models through small perturbations.
method Developed a continuous-time particle system (Abram) to approximate the gradient flow of the Bayesian adversarial robustness problem.
result Abram approximates the minimizer of the Bayesian adversarial robustness problem under certain assumptions.
New theory for area of Legendrian surfaces, proving smoothness and variational results.
problem Understanding the area of Legendrian surfaces under constraints.
method Introducing PHSLVs, proving sequential compactness, regularity, and variational results.
result Generalized regularity theory for Legendrian surfaces, achieving variational minima.
The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a generalization that allows a limited notion of arbitrage in the market while still…
SGD finds global optima in WGANs for 1-layer generators.
problem Training GANs with WGANs requires global optimality, which is hard.
method Used SGD to train 1-layer generator networks in WGANs.
result SGD converges to global solution in polynomial time and sample complexity.
The paper improves the empirical bootstrap method for non-normal estimators.
problem Theoretical properties of empirical bootstrap for non-asymptotically normal estimators.
method Establishing limiting distribution, deriving consistency conditions, proposing alternative methods.
result The empirical bootstrap method can be asymptotically consistent under stability conditions.
AAS optimizes neural network PDE approximations by adaptively sampling.
problem Statistical errors from random samples in neural network PDE approximations.
method Minmax formulation to optimize neural network and training set samples.
result Reduces Monte Carlo approximation error for a given sample size.
Paper accelerates conformal prediction by using approximate leave-one-out estimators.
problem Limited computational cost for conformal prediction.
method Incorporates approximate leave-one-out estimators to accelerate conformal prediction.
result ALO-based methods achieve comparable coverage and efficiency to exact methods but with significantly reduced runtime.
Paper characterizes phase transition of TV minimization for sparse-gradient signal recovery.
problem Characterizing phase transitions of TV minimization for sparse-gradient signal recovery.
method Combines AMP conjectured phase transition curve and high-dimensional convex geometry.
result Fully characterizes the phase transition curve of TV minimization.
This work finds mixed equilibria in zero-sum games using interacting particle dynamics.
problem Finding mixed equilibrium points in continuous minmax games.
method A method based on entropic regularisation of two-layer zero-sum games with interacting particle dynamics.
result The sequence of empirical measures of the particle system satisfies a large deviation principle as the number of particles grows to infinity, implying convergence of the empirical measure and the Nikaidô-Isoda error.
Stability of Morse index for Yang-Mills connections in 4D.
problem Stability of critical points in Yang-Mills energy relaxation.
method Establishing lower semi-continuity of Morse index and upper continuity of Morse index plus nullity.
result Yang-Mills fields are more stable than harmonic maps in 4D.
A new method controls risk for set predictors using cross-validation.
problem Inefficient set predictors when data limited.
method Cross-validation conformal risk control (CV-CRC).
result CV-CRC offers theoretical guarantees and reduces set size.
The paper constructs critical points of area using min-max method with penalization and viscosity.
problem Constructing critical points of minimal surface area using relaxed functional.
method Min-max construction with penalization and viscosity method.
result Critical points converge to smooth minimal immersions under entropy condition.
Paper proposes a new approach to improve WGAN training and achieves state-of-the-art results.
problem Difficulty in training GANs, especially Wasserstein GANs.
method Introduces a consistency term to enforce Lipschitz continuity in WGAN training.
result Achieves inception score of more than 5.0 with only 1,000 CIFAR-10 images and exceeds 90% accuracy on CIFAR-10 with 4,000 labeled images.
Study on bandits with fading memory, improving regret bounds.
problem Stochastic multi-armed bandit problem with dependent samples.
method Developed a $\cC-$Mix Improved UCB algorithm and analyzed regret bounds in two scenarios.
result Regret bounds similar to independent case in slow mixing scenario, with an additive term.
New method improves support estimation for unknown distributions.
problem Estimating the support size of an unknown distribution.
method Regularized Weighted Chebyshev Approximations, joint optimization of bias and variance, linear programming.
result Significant improvements in worst-case risk for synthetic data and accurate bacterial genus estimation for microbiome data.
Study analyzes symmetric two-armed Bernoulli bandit problem with zero mean gap.
problem Analyzing symmetric two-armed Bernoulli bandit problem with zero mean gap.
method Associated with a solution of a linear heat equation, compute leading order terms of minmax optimal regret and pseudoregret.
result Explicitly compute leading order terms in three scaling regimes for the gap.
Proposes an adversarial algorithm to learn unbiased representations via HGR coefficient.
problem Learning fair representations without sensitive attribute information.
method Adversarial algorithm using Hirschfeld-Gebelein-Renyi (HGR) maximal correlation coefficient.
result Significant improvements in bias mitigation compared to existing methods.
Structure-preserving GANs learn distributions with group symmetry efficiently.
problem Learning distributions with group symmetry efficiently.
method Developed structure-preserving GANs by reducing the discriminator space and designing structured generators.
result Significantly improved sample fidelity and diversity in small data regimes.
GANs can learn hierarchical distributions in real-world images efficiently.
problem Understanding and efficiently learning complex, real-world distributions with GANs.
method Formally studying how GANs can learn hierarchically generated distributions close to real-life image distributions using SGDA.
result Training GANs via SGDA can efficiently learn distributions with a 'forward super-resolution' structure, both in sample and time complexities.
Unified framework for adversarial attacks using min-max optimization.
problem Improving adversarial robustness and attack generation.
method General framework of min-max optimization over multiple domains.
result Substantial attack improvement and robustness improvement.
iWGAN improves GANs by stabilizing training and preventing mode collapse.
problem Stable and effective training of GANs with mode collapse.
method iWGAN combines auto-encoders and WGANs using iterative primal dual optimization.
result iWGAN provides a clear stopping criterion and mitigates mode collapse.
SMP estimator improves density and logistic regression under misspecification.
problem Improper estimator for optimal excess risk in misspecified models.
method SMP minimizes a new excess risk bound for statistical learning.
result SMP achieves optimal excess risk of O((d+B2R2)/n) for logistic regression. Improved iterative methods for risk parity portfolio weights.
problem Solving for portfolio weights in risk parity allocation.
method Enhanced CCD and Newton methods, including a rescaling step and improved initial guess.
result Improved CCD method is the best, three times faster with 40% fewer iterations.
Paper introduces stochastic mesh methods for efficient CVA computation.
problem Efficient computation of CVA for large systems using Monte Carlo methods.
method Introduces two stochastic mesh methods for CVA computation.
result Demonstrates the rate of convergence of the methods to real CVA values.
The study connects Gaussian quadrature methods to sigma-point methods in filtering and smoothing.
problem Understanding the relationship between Gaussian quadrature and sigma-point methods.
method Interpreting sigma-point methods as Gaussian quadrature methods with specific covariance functions, and discussing criteria for selecting sigma-point locations.
result Many sigma-point methods can be seen as Gaussian quadrature methods with specific covariance functions, and this interpretation extends to multivariate Gauss--Hermite integration methods and related spherical cubature rules.
A new method combines Laplace and Variational Bayes for scalable inference.
problem Complex models and large datasets make exact inference infeasible.
method Low-Rank Variational Bayes Correction (VBC) using Laplace method and Variational Bayes correction in a lower dimension.
result The method ensures scalability in both model complexity and data size.
Unified framework for model explanation methods based on feature removal.
problem Unclear relationships and preferences among various model explanation methods.
method Characterizes removal-based explanations along three dimensions.
result Unified 26 existing methods, including widely used approaches.