Related papers: Local Search for Solving Satisfiability of Polynom…

Generating proofs of unsatisfiability is a valuable capability of most SAT solvers, and is an active area of research for SMT solvers. This paper introduces the first method to efficiently generate proofs of unsatisfiability specifically…

The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as…

Multivariate analysis of fMRI data has benefited substantially from advances in machine learning. Most recently, a range of probabilistic latent variable models applied to fMRI data have been successful in a variety of tasks, including…

Large language models (LLMs) have revolutionized natural language processing (NLP) by excelling at understanding and generating human-like text. However, their widespread deployment can be prohibitively expensive. SortedNet is a recent…

In this paper, we introduce a powerful technique based on Leave-one-out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for…

With the increasing number of parameters in large pre-trained models, LoRA as a parameter-efficient fine-tuning(PEFT) method is widely used for not adding inference overhead. The LoRA method assumes that weight changes during fine-tuning…

In bracket algebra, the calculation of invariant division and invariant Gr\"{o}bner basis proposed in \cite{li 2014} rely on straightening algorithm. Until now, there are at least three different types of straightening algorithms, among…

Non-stationarity is one thorny issue in cooperative multi-agent reinforcement learning (MARL). One of the reasons is the policy changes of agents during the learning process. Some existing works have discussed various consequences caused by…

We present a randomized Local Computation Algorithm (LCA) with query complexity $poly(\Delta) \cdot \log n$ for the Maximal Independent Set (MIS) problem. That is, the algorithm determines whether each node is in the computed MIS or not…

We propose a symbolic-numeric algorithm to count the number of solutions of a polynomial system within a local region. More specifically, given a zero-dimensional system $f_1=\cdots=f_n=0$, with $f_i\in\mathbb{C}[x_1,\ldots,x_n]$, and a…

Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…

Recent research has shown that piecewise smooth (PS) functions can be approximated by piecewise linear functions with second order error in the distance to a given reference point. A semismooth Newton type algorithm based on successive…

It is the main goal of this paper to propose a novel method to perform matrix completion on-line. Motivated by a wide variety of applications, ranging from the design of recommender systems to sensor network localization through seismic…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

Boolean satisfiability is a propositional logic problem of interest in multiple fields, e.g., physics, mathematics, and computer science. Beyond a field of research, instances of the SAT problem, as it is known, require efficient solution…

Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…

In this paper, we consider constrained optimization problems with convex, smooth objective and constraints. We propose a new stochastic gradient algorithm, called the Stochastic Moving Ball Approximation (SMBA) method, to solve this class…

In this paper, we propose SubLoRA, a rank determination method for Low-Rank Adaptation (LoRA) based on submodular function maximization. In contrast to prior approaches, such as AdaLoRA, that rely on first-order (linearized) approximations…

Let $f:2^{E} \rightarrow \mathbb{Z}_+$ be a submodular function on a ground set $E = [n]$, and let $P(f)$ denote its extended polymatroid. Given a direction $d \in \mathbb{Z}^n$ with at least one positive entry, the line search problem is…

We consider in this paper a class of single-ratio fractional minimization problems, in which the numerator part of the objective is the sum of a nonsmooth nonconvex function and a smooth nonconvex function while the denominator part is a…