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We introduce a comprehensive Linguistic Benchmark designed to evaluate the limitations of Large Language Models (LLMs) in domains such as logical reasoning, spatial intelligence, and linguistic understanding, among others. Through a series…

Large Language Models (LLMs) have demonstrated remarkable performance across diverse domains. However, effectively leveraging their vast knowledge for training smaller downstream models remains an open challenge, especially in domains like…

This paper deals with sliding mode control for multivariable polytopic uncertain systems. We provide systematic procedures to design variable structure controllers (VSCs) and unit-vector controllers (UVCs). Based on suitable representations…

Large Language Models (LLMs) are a powerful technology that augment human skill to create new opportunities, akin to the development of steam engines and the internet. However, LLMs come with a high cost. They require significant computing…

Large Language Models have seen rapid progress in capability in recent years; this progress has been accelerating and their capabilities, measured by various benchmarks, are beginning to approach those of humans. There is a strong demand to…

The paper introduces a class of distances for linear behaviors over finite time horizons. These distances allow for comparisons between finite-horizon linear behaviors represented by matrices of possibly different dimensions. They remain…

Based on the foundation of Large Language Models (LLMs), Multilingual LLMs (MLLMs) have been developed to address the challenges faced in multilingual natural language processing, hoping to achieve knowledge transfer from high-resource…

Large language models (LLMs) have emerged as powerful tools for addressing a wide range of general inquiries and tasks. Despite this, fine-tuning aligned LLMs on smaller, domain-specific datasets, critical to adapting them to specialized…

Large language models (LLMs) have become the secret ingredient driving numerous industrial applications, showcasing their remarkable versatility across a diverse spectrum of tasks. From natural language processing and sentiment analysis to…

This paper presents a novel framework for stabilizing nonlinear systems represented in state-dependent form. We first reformulate the nonlinear dynamics as a state-dependent parameter-varying model and synthesize a stabilizing controller…

Due to the remarkable language understanding and generation abilities of large language models (LLMs), their use in educational applications has been explored. However, little work has been done on investigating the pedagogical ability of…

This paper is devoted to stability analysis of discrete-time delay systems based on a set of Lyapunov-Krasovskii functionals. New multiple summation inequalities are derived that involve the famous discrete Jensen's and Wirtinger's…

Since the rise of Large Language Models (LLMs) a couple of years ago, researchers in metaheuristics (MHs) have wondered how to use their power in a beneficial way within their algorithms. This paper introduces a novel approach that…

The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…

Large language models (LLMs) represent a new paradigm for processing unstructured data, with applications across an unprecedented range of domains. In this paper, we address, through two arguments, whether the development and application of…

This paper is concerned with the absolute stability analysis of discrete-time feedback systems with slope-restricted nonlinearities. By employing static O'Shea-Zames-Falb multipliers in the framework of integral quadratic constraints, we…

In this short article, some properties of matrices of moving least-squares approximation have been proven.The used technique is based on singular-value decomposition and inequalities for singular-values. Some inequalities for the norm of…

Large Language Models (LLMs) have made significant progress in reasoning, demonstrating their capability to generate human-like responses. This study analyzes the problem-solving capabilities of LLMs in the domain of thermodynamics. A…

A central question in verification is characterizing when a system has invariants of a certain form, and then synthesizing them. We say a system has a $k$ linear invariant, $k$-LI in short, if it has a conjunction of $k$ linear (non-strict)…

Large language models (LLMs) are increasingly deployed as the service backend for LLM-integrated applications such as code completion and AI-powered search. LLM-integrated applications serve as middleware to refine users' queries with…