arXiv - CS - Symbolic Computation最新文献_第10页

Deep Neural Network for Constraint Acquisition through Tailored Loss Function 通过定制损失函数获取约束的深度神经网络

arXiv - CS - Symbolic Computation Pub Date : 2024-03-04 DOI: arxiv-2403.02042

Eduardo Vyhmeister, Rocio Paez, Gabriel Gonzalez

引用次数: 0

Communication Optimal Unbalanced Private Set Union 通信最优非平衡私集联盟

arXiv - CS - Symbolic Computation Pub Date : 2024-02-26 DOI: arxiv-2402.16393

Jean-Guillaume DumasUGA, LJK, CASC, Alexis GalanCASC, Bruno GrenetCASC, Aude MaignanCASC, Daniel S. Roche

{"title":"Communication Optimal Unbalanced Private Set Union","authors":"Jean-Guillaume DumasUGA, LJK, CASC, Alexis GalanCASC, Bruno GrenetCASC, Aude MaignanCASC, Daniel S. Roche","doi":"arxiv-2402.16393","DOIUrl":"https://doi.org/arxiv-2402.16393","url":null,"abstract":"We consider the private set union (PSU) problem, where two parties each hold\u0000a private set of elements, and they want one of the parties (the receiver) to\u0000learn the union of the two sets and nothing else. Our protocols are targeted\u0000for the unbalanced case where the receiver's set size is larger than the\u0000sender's set size, with the goal of minimizing the costs for the sender both in\u0000terms of communication volume and local computation time. This setting is\u0000motivated by applications where the receiver has significantly more data (input\u0000set size) and computational resources than the sender which might be realized\u0000on a small, low-power device. Asymptotically, we achieve communication cost\u0000linear in the sender's (smaller) set size, and computation costs for sender and\u0000receiver which are nearly-linear in their respective set sizes. To our\u0000knowledge, ours is the first algorithm to achieve nearly-linear communication\u0000and computation for PSU in this unbalanced setting. Our protocols utilize fully\u0000homomorphic encryption (FHE) and, optionally, linearly homomorphic encryption\u0000(LHE) to perform the necessary computations while preserving privacy. The\u0000underlying computations are based on univariate polynomial arithmetic realized\u0000within homomorphic encryption, namely fast multiplication, modular reduction,\u0000and multi-point evaluation. These asymptotically fast HE polynomial arithmetic\u0000algorithms may be of independent interest.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139977247","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

Optimal Pseudorandom Generators for Low-Degree Polynomials Over Moderately Large Fields 中等大字段上低度多项式的最佳伪随机发生器

arXiv - CS - Symbolic Computation Pub Date : 2024-02-19 DOI: arxiv-2402.11915

Ashish Dwivedi, Zeyu Guo, Ben Lee Volk

引用次数: 0

Fast interpolation and multiplication of unbalanced polynomials 非平衡多项式的快速插值和乘法

arXiv - CS - Symbolic Computation Pub Date : 2024-02-15 DOI: arxiv-2402.10139

Pascal Giorgi, Bruno Grenet, Armelle Perret du Cray, Daniel S. Roche

引用次数: 0

Computing Krylov iterates in the time of matrix multiplication 在矩阵乘法时间内计算克雷洛夫迭代

arXiv - CS - Symbolic Computation Pub Date : 2024-02-12 DOI: arxiv-2402.07345

Vincent Neiger, Clément Pernet, Gilles Villard

{"title":"Computing Krylov iterates in the time of matrix multiplication","authors":"Vincent Neiger, Clément Pernet, Gilles Villard","doi":"arxiv-2402.07345","DOIUrl":"https://doi.org/arxiv-2402.07345","url":null,"abstract":"Krylov methods rely on iterated matrix-vector products $A^k u_j$ for an\u0000$ntimes n$ matrix $A$ and vectors $u_1,ldots,u_m$. The space spanned by all\u0000iterates $A^k u_j$ admits a particular basis -- the emph{maximal Krylov basis}\u0000-- which consists of iterates of the first vector $u_1, Au_1, A^2u_1,ldots$,\u0000until reaching linear dependency, then iterating similarly the subsequent\u0000vectors until a basis is obtained. Finding minimal polynomials and Frobenius\u0000normal forms is closely related to computing maximal Krylov bases. The fastest\u0000way to produce these bases was, until this paper, Keller-Gehrig's 1985\u0000algorithm whose complexity bound $O(n^omega log(n))$ comes from repeated\u0000squarings of $A$ and logarithmically many Gaussian eliminations. Here\u0000$omega>2$ is a feasible exponent for matrix multiplication over the base\u0000field. We present an algorithm computing the maximal Krylov basis in\u0000$O(n^omegaloglog(n))$ field operations when $m in O(n)$, and even\u0000$O(n^omega)$ as soon as $min O(n/log(n)^c)$ for some fixed real $c>0$. As a\u0000consequence, we show that the Frobenius normal form together with a\u0000transformation matrix can be computed deterministically in $O(n^omega\u0000loglog(n)^2)$, and therefore matrix exponentiation~$A^k$ can be performed in\u0000the latter complexity if $log(k) in O(n^{omega-1-varepsilon})$, for\u0000$varepsilon>0$. A key idea for these improvements is to rely on fast\u0000algorithms for $mtimes m$ polynomial matrices of average degree $n/m$,\u0000involving high-order lifting and minimal kernel bases.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139767521","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

Ensuring trustworthy and ethical behaviour in intelligent logical agents 确保智能逻辑代理的可信和道德行为

arXiv - CS - Symbolic Computation Pub Date : 2024-02-12 DOI: arxiv-2402.07547

Stefania Costantini

引用次数: 0

Towards a Parallel Summation Algorithm 迈向并行求和算法

arXiv - CS - Symbolic Computation Pub Date : 2024-02-07 DOI: arxiv-2402.04684

Shaoshi Chen, Ruyong Feng, Manuel Kauers, Xiuyun Li

引用次数: 0

SymbolicAI: A framework for logic-based approaches combining generative models and solvers SymbolicAI：结合生成模型和求解器的基于逻辑的方法框架

arXiv - CS - Symbolic Computation Pub Date : 2024-02-01 DOI: arxiv-2402.00854

Marius-Constantin Dinu, Claudiu Leoveanu-Condrei, Markus Holzleitner, Werner Zellinger, Sepp Hochreiter

{"title":"SymbolicAI: A framework for logic-based approaches combining generative models and solvers","authors":"Marius-Constantin Dinu, Claudiu Leoveanu-Condrei, Markus Holzleitner, Werner Zellinger, Sepp Hochreiter","doi":"arxiv-2402.00854","DOIUrl":"https://doi.org/arxiv-2402.00854","url":null,"abstract":"We introduce SymbolicAI, a versatile and modular framework employing a\u0000logic-based approach to concept learning and flow management in generative\u0000processes. SymbolicAI enables the seamless integration of generative models\u0000with a diverse range of solvers by treating large language models (LLMs) as\u0000semantic parsers that execute tasks based on both natural and formal language\u0000instructions, thus bridging the gap between symbolic reasoning and generative\u0000AI. We leverage probabilistic programming principles to tackle complex tasks,\u0000and utilize differentiable and classical programming paradigms with their\u0000respective strengths. The framework introduces a set of polymorphic,\u0000compositional, and self-referential operations for data stream manipulation,\u0000aligning LLM outputs with user objectives. As a result, we can transition\u0000between the capabilities of various foundation models endowed with zero- and\u0000few-shot learning capabilities and specialized, fine-tuned models or solvers\u0000proficient in addressing specific problems. In turn, the framework facilitates\u0000the creation and evaluation of explainable computational graphs. We conclude by\u0000introducing a quality measure and its empirical score for evaluating these\u0000computational graphs, and propose a benchmark that compares various\u0000state-of-the-art LLMs across a set of complex workflows. We refer to the\u0000empirical score as the \"Vector Embedding for Relational Trajectory Evaluation\u0000through Cross-similarity\", or VERTEX score for short. The framework codebase\u0000and benchmark are linked below.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139666345","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

Creative Telescoping for Hypergeometric Double Sums 超几何双和的创造性伸缩

arXiv - CS - Symbolic Computation Pub Date : 2024-01-29 DOI: arxiv-2401.16314

Peter Paule, Carsten Schneider

引用次数: 0

Symbolic Equation Solving via Reinforcement Learning 通过强化学习解符号方程

arXiv - CS - Symbolic Computation Pub Date : 2024-01-24 DOI: arxiv-2401.13447

Lennart Dabelow, Masahito Ueda

引用次数: 0