Related papers: Under-approximation of the Greatest Fixpoints in R…
We study the best approximation problem: \[ \displaystyle \min_{\alpha\in \mathbb R^m}\max_{1\leq i\leq n}\left|y_i -\sum_{j=1}^m \alpha_j \Gamma_j ({\bf x}_i) \right|. \] Here: $\Gamma:=\left\{\Gamma_1,...,\Gamma_m\right\}$ is a list of…
In Monte Carlo simulations of lattice field theory with a $\theta$ term, one confronts the complex weight problem, or the sign problem. This is circumvented by performing the Fourier transform of the topological charge distribution $P(Q)$.…
Maximizing submodular objectives under constraints is a fundamental problem in machine learning and optimization. We study the maximization of a nonnegative, non-monotone $\gamma$-weakly DR-submodular function over a down-closed convex…
Large Language Models (LLMs) generate functionally correct solutions but often fall short in code efficiency, a critical bottleneck for real-world deployment. In this paper, we introduce a novel test-time iterative optimization framework to…
Hyperproperties extend trace properties to express properties of sets of traces, and they are increasingly popular in specifying various security and performance-related properties in domains such as cyber-physical systems, smart grids, and…
This paper deals with some nonlinear problems which exponential and biexponential decays are involved in. A proof of the quasiconvexity of the error function in some of these problems of optimization is presented. This proof is restricted…
There has been a recent critical need to study fairness and bias in machine learning (ML) algorithms. Since there is clearly no one-size-fits-all solution to fairness, ML methods should be developed alongside bias mitigation strategies that…
Entity alignment (EA) aims at identifying equivalent entity pairs across different knowledge graphs (KGs) that refer to the same real-world identity. To circumvent the shortage of seed alignments provided for training, recent EA models…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
Auto-active program verification rests on the ability to effectively the translation from annotated programs into verification conditions that are then discharged by automated theorem provers in the background. Characteristic such tools,…
We study the sign problem in lattice field theory with a $\theta$ term. We apply the maximum entropy method (MEM) to flattening phenomenon of the free energy density $f(\theta)$, which originates from the sign problem. In our previous…
Large language models (LLMs) are increasingly explored for NP-hard combinatorial optimization problems, but most existing methods emphasize feasible-instance solution generation and do not explicitly address infeasibility detection. We…
Max-Plus Linear (MPL) systems are an algebraic formalism with practical applications in transportation networks, manufacturing and biological systems. In this paper, we investigate the problem of automatically analyzing the properties of…
The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual…
Recently, formal verification of deep neural networks (DNNs) has garnered considerable attention, and over-approximation based methods have become popular due to their effectiveness and efficiency. However, these strategies face challenges…
In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more…
For a continuous function $f$ defined on a closed and bounded domain, there is at least one maximum and one minimum. First, we introduce some preliminaries which are necessary through the paper. We then present an algorithm, which is…
Optimizing non-convex functions is a fundamental challenge across machine learning and combinatorial optimization. We introduce and study $\gamma$-weakly $\theta$-up-concavity, a novel first-order condition that characterizes a broad class…
Conformance checking techniques let us find out to what degree a process model and real execution data correspond to each other. In recent years, alignments have proven extremely useful in calculating conformance statistics. Most techniques…
One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…