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Rates of (T-)asymptotic regularity of the generalized Krasnoselskii-Mann-type iteration

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arXiv 2025年

作者： Firmino, Paulo Leuştean, Laurenţiu Departamento de Matemática Faculdade de Ciências Universidade de Lisboa Portugal LOS Faculty of Mathematics and Computer Science University of Bucharest Romania Simion Stoilow Institute of Mathematics The Romanian Academy Romania Institute for Logic and Data Science Bucharest Romania

In this paper we use proof mining methods to compute rates of (T-)asymptotic regularity of the generalized Krasnoselskii-Mann-type iteration associated to a nonexpansive mapping T: X → X in a uniformly convex normed space X. For special choices of the parameter sequences, we obtain quadratic *** Codes 47H05, 47H09, 47J25 © 2025, CC BY.

关键词： Iterative methods

On the uniform convexity of the squared distance

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arXiv 2025年

作者： Sipoş, Andrei Department of Computer Science Faculty of Mathematics and Computer Science University of Bucharest Academiei 14 Bucharest010014 Romania Simion Stoilow Institute of Mathematics The Romanian Academy Calea Grivit ¸ei 21 Bucharest010702 Romania Institute for Logic and Data Science Popa Tatu 18 Bucharest010805 Romania

In 1983, Zalinescu showed that the squared norm of a uniformly convex normed space is uniformly convex on bounded subsets. We extend this result to the metric setting of uniformly convex hyperbolic spaces. We derive applications to the convergence of shadow sequences and to proximal *** Codes 51F99, 52A55, 53C23 Copyright © 2025, The Authors. All rights reserved.

关键词： Hyperbolic functions

On modular representations of C-recursive integer sequences

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arXiv 2025年

作者： Prunescu, Mihai Shunia, Joseph M. Romania Institute of Logic and Data Science Bucharest Romania Simion Stoilow Institute of Mathematics of the Romanian Academy Research unit 5 P. O. Box 1-764 BucharestRO-014700 Romania Veeam Software ColumbusOH United States

Prunescu and Sauras-Altuzarra showed that all C-recursive sequences of natural numbers have an arithmetic div-mod representation that can be derived from their generating function. This representation consists of computing the quotient of two exponential polynomials and taking the remainder of the result modulo a third exponential polynomial, and works for all integers n ≥ 1. Using a different approach, Prunescu proved the existence of two other representations, one of which is the mod-mod representation, consisting of two successive remainder computations. This result has two weaknesses: (i) the representation works only ultimately, and (ii) a correction term must be added to the first exponential polynomial. We show that a mod-mod representation without inner correction term holds for all integers n ≥ 1. This follows directly from the div-mod representation by an arithmetic short-cut from *** Codes 11B37 (primary), 39A06 (secondary) © 2025, CC BY.

关键词： Digital arithmetic

Empowering LLMs with logical Reasoning: A Comprehensive Survey

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arXiv 2025年

作者： Cheng, Fengxiang Li, Haoxuan Liu, Fenrong van Rooij, Robert Zhang, Kun Lin, Zhouchen Institute for Logic Language and Computation University of Amsterdam Netherlands Center for Data Science Peking University China Machine Learning Department MBZUAI Department of Philosophy Tsinghua University China Department of Philosophy CMU United States Institute for Artificial Intelligence Peking University China Peng Cheng Laboratory China National Key Lab of General AI School of Intelligence Science and Technology Peking University China

Large language models (LLMs) have achieved remarkable successes on various natural language tasks. However, recent studies have found that there are still significant challenges to the logical reasoning abilities of LLMs. This paper summarizes and categorizes the main challenges into two aspects: (1) logical question answering, LLMs often fail to generate the correct answer within complex logical problem which requires sophisticated deductive, inductive or abductive reasoning given a collection of premises and constrains. (2) logical consistency, LLMs are prone to producing responses contradicting themselves across different questions. For example, a state-of-the-art Macaw question-answering LLM answers Yes to both questions Is a magpie a bird? and Does a bird have wings? but answers No to Does a magpie have wings?. To facilitate this research direction, we comprehensively investigate the most cutting-edge methods and propose detailed taxonomies of these methods. Specifically, to accurately answer complex logic questions, previous methods can be categorized based on reliance on external solvers, prompts, pretraining, and fine-tuning. To avoid logical contradictions, we discuss concepts and solutions of various logical consistencies, including implication, negation, transitivity, factuality consistency, and their composites. In addition, we review commonly used benchmark datasets and evaluation metrics, and discuss promising research directions, such as extensions to modal logic to account for uncertainty, and efficient algorithms satisfying multiple logical consistencies simultaneously. © 2025, CC BY.

关键词： Birds

An Overview of AI Techniques in DYNABIC Project 8

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An Overview of AI Techniques in DYNABIC Project

8th International Joint Conference on Rules and Reasoning, RuleML+RR-Companion 2024

作者： Paduraru, Ciprian Cristea, Rares Stefanescu, Alin University of Bucharest Romania Institute for Logic and Data Science Romania

We present an overview of the AI techniques used in Horizon Project No. 101070455 DYNABIC (Dynamic business continuity and response of critical systems against advanced cyber-physical threats). The project, which started in December 2022 and spans three years, aims to enhance European critical services’ resilience and business continuity against cyber-physical threats. The project focuses on real-time prediction, assessment, and mitigation of threats, as well as automated optimization and orchestration strategies for response and prevention. Demonstrations are conducted in four industry-based case studies, simulating attacks on intelligent transportation services, electric vehicle charging stations, 5G telecommunication infrastructure, and healthcare services. Each infrastructure is modeled using a digital twin, which simulates business processes and allows user input for control. The paper focuses on one of the uses of AI within DYNABIC involving large-language models fine-tuned to assist cybersecurity experts. © 2024 Copyright for this paper by its authors.

关键词： 5G mobile communication systems

Large Physics Models: Towards a collaborative approach with Large Language Models and Foundation Models

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arXiv 2025年

作者： Barman, Kristian G. Caron, Sascha Sullivan, Emily de Regt, Henk W. de Austri, Roberto Ruiz Boon, Mieke Färber, Michael Fröse, Stefan Hasibi, Faegheh Ipp, Andreas Kapoor, Rukshak Kasieczka, Gregor Kostić, Daniel Krämer, Michael Golling, Tobias Lopez, Luis G. Marco, Jesus Otten, Sydney Pawlowski, Pawel Vischia, Pietro Weber, Erik Weniger, Christoph CLPS - Centre for Logic and Philosophy of Science UGent Belgium IMAPP Radboud University and Nikhef NL Netherlands Utrecht University Netherlands Institute for Science in Society Radboud University Netherlands CSIC-UV Spain University of Twente Netherlands TU Dresden & ScaDS.AI Germany ErUM-Data-Hub & TU Dortmund University Germany Computing and Information Science Radboud University Netherlands TU Wien Austria Patiala India Universität Hamburg Germany Institute of Philosophy University of Leiden Netherlands RWTH Aachen University Germany University of Geneva Switzerland Munich Center for Mathematical Philosophy LMU Munich Germany CSIC-UC Spain Radboud University Netherlands Ippen Digital Germany Universidad de Oviedo ICTEA Spain GRAPPA Institute of Physics University of Amsterdam Netherlands

This paper explores ideas and provides a potential roadmap for the development and evaluation of physics-specific large-scale AI models, which we refer to as Large Physics Models (LPMs). These models, based on foundation models such as Large Language Models (LLMs) - trained on broad data - are tailored to address the unique demands of physics research. LPMs can function independently or as part of an integrated framework. This framework can incorporate specialized tools, including symbolic reasoning modules for mathematical manipulations, frameworks to analyse specific experimental and simulated data, and mechanisms for synthesizing insights from physical theories and scientific literature. We begin by examining whether the physics community should actively develop and refine dedicated models, rather than relying solely on commercial LLMs. We then outline how LPMs can be realized through interdisciplinary collaboration among experts in physics, computer science, and philosophy of science. To integrate these models effectively, we identify three key pillars: Development, Evaluation, and Philosophical Reflection. Development focuses on constructing models capable of processing physics texts, mathematical formulations, and diverse physical data. Evaluation assesses accuracy and reliability through testing and benchmarking. Finally, Philosophical Reflection encompasses the analysis of broader implications of LLMs in physics, including their potential to generate new scientific understanding and what novel collaboration dynamics might arise in research. Inspired by the organizational structure of experimental collaborations in particle physics, we propose a similarly interdisciplinary and collaborative approach to building and refining Large Physics Models. This roadmap provides specific objectives, defines pathways to achieve them, and identifies challenges that must be addressed to realise physics-specific large scale AI models. © 2025, CC BY.

关键词： Benchmarking

LLM-based methods for the creation of unit tests in game development 28th

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LLM-based methods for the creation of unit tests in game dev...

28th International Conference on Knowledge Based and Intelligent information and Engineering Systems, KES 2024

作者： Paduraru, Ciprian Staicu, Adelina Stefanescu, Alin University of Bucharest Department of Computer Science Romania Institute of Logic and Data Science Romania

Problems related to the quality of games, whether on the initial release or after updates, can lead to player dissatisfaction, media attention, and potential financial setbacks. These issues can stem from software bugs, performance bottlenecks, or security vulnerabilities. Despite these challenges, game developers often rely on manual playtesting, highlighting the need for more robust and automated processes in game development. This research explores the application of Large Language Models (LLMs) to automate the creation of unit tests in game development, focusing on strongly typed programming languages such as C++ and C#, which are widely used in the industry. The study focuses on fine-tuning Code Llama, an advanced code generation model, to address common scenarios in game development, including game engines and specific APIs or backends. Although the prototyping and evaluations primarily took place within the Unity game engine, the proposed methods can be adapted to other internal or publicly available solutions. The evaluation results demonstrate these methods' effectiveness in improving existing unit test suites or automatically generating new tests based on natural language descriptions of class contexts and targeted methods. © 2024 The Authors.

关键词： C++ (programming language)

Intuitionistic Propositional logic in Lean 8

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Intuitionistic Propositional Logic in Lean

8th Symposium on Working Formal Methods, FROM 2024

作者： Trufas, Dafina LOS Faculty of Mathematics and Computer Science University of Bucharest Institute for Logic and Data Science Bucharest Romania

In this paper we present a formalization of Intuitionistic Propositional logic in the Lean proof assistant. Our approach focuses on verifying two completeness proofs for the studied logical system, as well as exploring the relation between the two analyzed semantical paradigms - Kripke and algebraic. In addition, we prove a large number of theorems and derived deduction rules. © Dafina Trufas.

关键词： Computer circuits

CyberGuardian: An Interactive Assistant for Cybersecurity Specialists Using Large Language Models

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CyberGuardian: An Interactive Assistant for Cybersecurity Sp...

19th International Conference on Software Technologies, ICSOFT 2024

作者： Paduraru, Ciprian Patilea, Catalina Camelia Stefanescu, Alin Department of Computer Science University of Bucharest Romania Institute for Logic and Data Science Romania

ISBN: (纸本)9789897587061

Cybersecurity plays an important role in protecting people and critical infrastructure. Sectors such as energy, defense and healthcare are increasingly at risk from cyber threats. To address these challenges, dedicated Security Operations Centers (SOCs) continuously monitor threats and respond to critical issues. Our research focuses on the use of Large Language Models (LLMs) to optimize the tasks of SOCs and to support security professionals. In this work, we propose a framework, which we call CyberGuardian, whose main goal is to provide a chatbot application along with a set of tools to support SOC analysts in real-time cybersecurity tasks. We use state-of-the-art LLM techniques and start from a Llama 2 model, then fine-tune the base model using a new dataset containing mainly cybersecurity topics. The CyberGuardian framework has a plugin architecture that integrates processes such as Retrieval Augmented Generation (RAG), safeguard methods for interaction between human user and chatbot, integration with tools to manage tasks such as database interactions, code generation and execution, and plotting graphs just by specifying the task in a natural language. The work, along with the dataset we collected and reusable code to update or customize, is made available to the cybersecurity community as open source. © 2024 by SCITEPRESS – science and Technology Publications, Lda.

关键词： Critical infrastructures