The paper establishes conditions for QUBO formulations of combinatorial optimization problems that guarantee valid binary and feasible local minimizers using gradient-based methods.

This paper proves the conjecture that Local SGD outperforms Mini-batch SGD under bounded second-order heterogeneity for general convex objectives, improving the convergence guarantee and lower bounds.

The paper introduces Inconsistency-Aware Minimization (IAM), a novel training objective that uses a label-free measure called local inconsistency to improve model generalization, particularly in semi-…

This paper presents a local computation algorithm to approximate the top eigenvector of a symmetric matrix with entries between -1 and 1, building on Swartworth and Woodruff's work.

This paper derives the gradient of the Wolkowicz-Styan upper bound on the maximum eigenvalue of the cross-entropy loss Hessian in three-layer NNs to characterize directions leading to flat minima and…

This paper introduces Curvature-Weighted Gradient Diversity (CWGD), a geometry-aware measure for optimization noise that reduces the asymptotic optimization error floor by up to a factor of two compar…

This paper simplifies the proof of the bound on the target dimension for reducing the dimension of high-dimensional polygonal curves using random projections, extending it to various distance measures…

The paper introduces local Preferential Bayesian Optimization (PBO) methods that adapt high-dimensional Bayesian Optimization techniques, such as trust-region and derivative-informed local search, to…

The paper introduces Singularity-aware Adam (S-Adam), a novel optimizer that stabilizes deep learning training in non-smooth loss landscapes by dynamically damping updates based on local geometric ins…

This paper settles the complexity of three sketching problems in graphs and distributions.

This paper introduces approximation-preserving coresets, which provide weaker guarantees than strong coresets but stronger guarantees than weak coresets for preserving the costs of good solutions in b…

This paper constructs an epsilon-cover of the joint value set of m constant-degree polynomials over a convex set H in the linfty-norm, with size n^(O(log(mn)/ε^2)), given that the polynomials have a c…

This paper proves that the minimum edge-outerplanarity of a planar graph can be computed in polynomial time.

The paper introduces a method to efficiently detect 'essential' constraints in Boolean MinCSPs, significantly reducing the search space for solving these problems and providing a dichotomy theorem for…

This paper introduces structured cut sets, a novel preprocessing technique for Maximum k-Cut, and extends existing techniques from Maximum Cut. The rules are optimality-preserving and yield significan…

This paper systematically explores the convex polygon reconstruction problem with specified sets of features, contributing new testing algorithms and hardness results.