arXiv - CS - Symbolic Computation最新文献_第6页

Automated Loss function Search for Class-imbalanced Node Classification 用于类别不平衡节点分类的自动损失函数搜索

arXiv - CS - Symbolic Computation Pub Date : 2024-05-23 DOI: arxiv-2405.14133

Xinyu Guo, Kai Wu, Xiaoyu Zhang, Jing Liu

引用次数: 0

The Recovery of $λ$ from a Hilbert Polynomial 从希尔伯特多项式中找回 $λ$

arXiv - CS - Symbolic Computation Pub Date : 2024-05-21 DOI: arxiv-2405.12886

Joseph Donato, Monica Lewis

引用次数: 0

Strided Difference Bound Matrices 跨距差分约束矩阵

arXiv - CS - Symbolic Computation Pub Date : 2024-05-18 DOI: arxiv-2405.11244

Arjun Pitchanathan, Albert Cohen, Oleksandr Zinenko, Tobias Grosser

引用次数: 0

Simulating Petri nets with Boolean Matrix Logic Programming 用布尔矩阵逻辑编程模拟 Petri 网

arXiv - CS - Symbolic Computation Pub Date : 2024-05-18 DOI: arxiv-2405.11412

Lun Ai, Stephen H. Muggleton, Shi-Shun Liang, Geoff S. Baldwin

{"title":"Simulating Petri nets with Boolean Matrix Logic Programming","authors":"Lun Ai, Stephen H. Muggleton, Shi-Shun Liang, Geoff S. Baldwin","doi":"arxiv-2405.11412","DOIUrl":"https://doi.org/arxiv-2405.11412","url":null,"abstract":"Recent attention to relational knowledge bases has sparked a demand for\u0000understanding how relations change between entities. Petri nets can represent\u0000knowledge structure and dynamically simulate interactions between entities, and\u0000thus they are well suited for achieving this goal. However, logic programs\u0000struggle to deal with extensive Petri nets due to the limitations of high-level\u0000symbol manipulations. To address this challenge, we introduce a novel approach\u0000called Boolean Matrix Logic Programming (BMLP), utilising boolean matrices as\u0000an alternative computation mechanism for Prolog to evaluate logic programs.\u0000Within this framework, we propose two novel BMLP algorithms for simulating a\u0000class of Petri nets known as elementary nets. This is done by transforming\u0000elementary nets into logically equivalent datalog programs. We demonstrate\u0000empirically that BMLP algorithms can evaluate these programs 40 times faster\u0000than tabled B-Prolog, SWI-Prolog, XSB-Prolog and Clingo. Our work enables the\u0000efficient simulation of elementary nets using Prolog, expanding the scope of\u0000analysis, learning and verification of complex systems with logic programming\u0000techniques.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141147582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Jacobi Stability Analysis for Systems of ODEs Using Symbolic Computation 利用符号计算对 ODE 系统进行雅可比稳定性分析

arXiv - CS - Symbolic Computation Pub Date : 2024-05-17 DOI: arxiv-2405.10578

Bo Huang, Dongming Wang, Jing Yang

{"title":"Jacobi Stability Analysis for Systems of ODEs Using Symbolic Computation","authors":"Bo Huang, Dongming Wang, Jing Yang","doi":"arxiv-2405.10578","DOIUrl":"https://doi.org/arxiv-2405.10578","url":null,"abstract":"The classical theory of Kosambi-Cartan-Chern (KCC) developed in differential\u0000geometry provides a powerful method for analyzing the behaviors of dynamical\u0000systems. In the KCC theory, the properties of a dynamical system are described\u0000in terms of five geometrical invariants, of which the second corresponds to the\u0000so-called Jacobi stability of the system. Different from that of the Lyapunov\u0000stability that has been studied extensively in the literature, the analysis of\u0000the Jacobi stability has been investigated more recently using geometrical\u0000concepts and tools. It turns out that the existing work on the Jacobi stability\u0000analysis remains theoretical and the problem of algorithmic and symbolic\u0000treatment of Jacobi stability analysis has yet to be addressed. In this paper,\u0000we initiate our study on the problem for a class of ODE systems of arbitrary\u0000dimension and propose two algorithmic schemes using symbolic computation to\u0000check whether a nonlinear dynamical system may exhibit Jacobi stability. The\u0000first scheme, based on the construction of the complex root structure of a\u0000characteristic polynomial and on the method of quantifier elimination, is\u0000capable of detecting the existence of the Jacobi stability of the given\u0000dynamical system. The second algorithmic scheme exploits the method of\u0000semi-algebraic system solving and allows one to determine conditions on the\u0000parameters for a given dynamical system to have a prescribed number of Jacobi\u0000stable fixed points. Several examples are presented to demonstrate the\u0000effectiveness of the proposed algorithmic schemes.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141147605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bridging Syntax and Semantics of Lean Expressions in E-Graphs 架起电子图表中精益表达语法与语义的桥梁

arXiv - CS - Symbolic Computation Pub Date : 2024-05-16 DOI: arxiv-2405.10188

Marcus Rossel, Andrés Goens

引用次数: 0

Generalized Holographic Reduced Representations 广义全息还原表征

arXiv - CS - Symbolic Computation Pub Date : 2024-05-15 DOI: arxiv-2405.09689

Calvin Yeung, Zhuowen Zou, Mohsen Imani

{"title":"Generalized Holographic Reduced Representations","authors":"Calvin Yeung, Zhuowen Zou, Mohsen Imani","doi":"arxiv-2405.09689","DOIUrl":"https://doi.org/arxiv-2405.09689","url":null,"abstract":"Deep learning has achieved remarkable success in recent years. Central to its\u0000success is its ability to learn representations that preserve task-relevant\u0000structure. However, massive energy, compute, and data costs are required to\u0000learn general representations. This paper explores Hyperdimensional Computing\u0000(HDC), a computationally and data-efficient brain-inspired alternative. HDC\u0000acts as a bridge between connectionist and symbolic approaches to artificial\u0000intelligence (AI), allowing explicit specification of representational\u0000structure as in symbolic approaches while retaining the flexibility of\u0000connectionist approaches. However, HDC's simplicity poses challenges for\u0000encoding complex compositional structures, especially in its binding operation.\u0000To address this, we propose Generalized Holographic Reduced Representations\u0000(GHRR), an extension of Fourier Holographic Reduced Representations (FHRR), a\u0000specific HDC implementation. GHRR introduces a flexible, non-commutative\u0000binding operation, enabling improved encoding of complex data structures while\u0000preserving HDC's desirable properties of robustness and transparency. In this\u0000work, we introduce the GHRR framework, prove its theoretical properties and its\u0000adherence to HDC properties, explore its kernel and binding characteristics,\u0000and perform empirical experiments showcasing its flexible non-commutativity,\u0000enhanced decoding accuracy for compositional structures, and improved\u0000memorization capacity compared to FHRR.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Vector-Symbolic Architecture for Event-Based Optical Flow 基于事件的光流矢量符号架构

arXiv - CS - Symbolic Computation Pub Date : 2024-05-14 DOI: arxiv-2405.08300

Hongzhi You, Yijun Cao, Wei Yuan, Fanjun Wang, Ning Qiao, Yongjie Li

{"title":"Vector-Symbolic Architecture for Event-Based Optical Flow","authors":"Hongzhi You, Yijun Cao, Wei Yuan, Fanjun Wang, Ning Qiao, Yongjie Li","doi":"arxiv-2405.08300","DOIUrl":"https://doi.org/arxiv-2405.08300","url":null,"abstract":"From a perspective of feature matching, optical flow estimation for event\u0000cameras involves identifying event correspondences by comparing feature\u0000similarity across accompanying event frames. In this work, we introduces an\u0000effective and robust high-dimensional (HD) feature descriptor for event frames,\u0000utilizing Vector Symbolic Architectures (VSA). The topological similarity among\u0000neighboring variables within VSA contributes to the enhanced representation\u0000similarity of feature descriptors for flow-matching points, while its\u0000structured symbolic representation capacity facilitates feature fusion from\u0000both event polarities and multiple spatial scales. Based on this HD feature\u0000descriptor, we propose a novel feature matching framework for event-based\u0000optical flow, encompassing both model-based (VSA-Flow) and self-supervised\u0000learning (VSA-SM) methods. In VSA-Flow, accurate optical flow estimation\u0000validates the effectiveness of HD feature descriptors. In VSA-SM, a novel\u0000similarity maximization method based on the HD feature descriptor is proposed\u0000to learn optical flow in a self-supervised way from events alone, eliminating\u0000the need for auxiliary grayscale images. Evaluation results demonstrate that\u0000our VSA-based method achieves superior accuracy in comparison to both\u0000model-based and self-supervised learning methods on the DSEC benchmark, while\u0000remains competitive among both methods on the MVSEC benchmark. This\u0000contribution marks a significant advancement in event-based optical flow within\u0000the feature matching methodology.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networks 利用 Kolmogorov-Arnold 网络建立柔性 EHD 泵的预测模型

arXiv - CS - Symbolic Computation Pub Date : 2024-05-13 DOI: arxiv-2405.07488

Yanhong Peng, Miao He, Fangchao Hu, Zebing Mao, Xia Huang, Jun Ding

引用次数: 0

Scalable Computation of Inter-Core Bounds Through Exact Abstractions 通过精确抽象实现内核间界限的可扩展计算

arXiv - CS - Symbolic Computation Pub Date : 2024-05-10 DOI: arxiv-2405.06387

Mohammed Aristide Foughali, Marius Mikučionis, Maryline Zhang

{"title":"Scalable Computation of Inter-Core Bounds Through Exact Abstractions","authors":"Mohammed Aristide Foughali, Marius Mikučionis, Maryline Zhang","doi":"arxiv-2405.06387","DOIUrl":"https://doi.org/arxiv-2405.06387","url":null,"abstract":"Real-time systems (RTSs) are at the heart of numerous safety-critical\u0000applications. An RTS typically consists of a set of real-time tasks (the\u0000software) that execute on a multicore shared-memory platform (the hardware)\u0000following a scheduling policy. In an RTS, computing inter-core bounds, i.e.,\u0000bounds separating events produced by tasks on different cores, is crucial.\u0000While efficient techniques to over-approximate such bounds exist, little has\u0000been proposed to compute their exact values. Given an RTS with a set of cores C\u0000and a set of tasks T , under partitioned fixed- priority scheduling with\u0000limited preemption, a recent work by Foughali, Hladik and Zuepke (FHZ) models\u0000tasks with affinity c (i.e., allocated to core c in C) as a Uppaal timed\u0000automata (TA) network Nc. For each core c in C, Nc integrates blocking (due to\u0000data sharing) using tight analytical formulae. Through compositional model\u0000checking, FHZ achieved a substantial gain in scalability for bounds local to a\u0000core. However, computing inter-core bounds for some events of interest E,\u0000produced by a subset of tasks TE with different affinities CE, requires model\u0000checking the parallel composition of all TA networks Nc for each c in CE, which\u0000produces a large, often intractable, state space. In this paper, we present a\u0000new scalable approach based on exact abstractions to compute exact inter-core\u0000bounds in a schedulable RTS, under the assumption that tasks in TE have\u0000distinct affinities. We develop a novel algorithm, leveraging a new query that\u0000we implement in Uppaal, that computes for each TA network Nc in NE an\u0000abstraction A(Nc) preserving the exact intervals within which events occur on\u0000c, therefore drastically reducing the state space. The scalability of our\u0000approach is demonstrated on the WATERS 2017 industrial challenge, for which we\u0000efficiently compute various types of inter-core bounds where FHZ fails to\u0000scale.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140927120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0