检索结果-内蒙古大学图书馆

Unifying AMP algorithms for Rotationally-Invariant Models

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Liu, Songbin Ma, Junjie The Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences China

This paper presents a unified framework for constructing Approximate Message Passing (AMP) algorithms for rotationally-invariant models. By employing a general iterative algorithm template and reducing it to long-memory Orthogonal AMP (OAMP), we systematically derive the correct Onsager terms of AMP algorithms. This approach allows us to rederive an AMP algorithm introduced by Fan and Opper et al., while shedding new light on the role of free cumulants of the spectral law. The free cumulants arise naturally from a recursive centering operation, potentially of independent interest beyond the scope of AMP. To illustrate the flexibility of our framework, we introduce two novel AMP variants and apply them to estimation in spiked models. © 2024, CC BY.

关键词： consensus algorithm

EduChain: A highly available education consortium blockchain platform based on Hyperledger Fabric

学校读者我要写书评

暂无评论

CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE 2023年第18期35卷

作者： Liang, Xiubo Zhao, Qian Zhang, Yanyu Liu, Hongyu Zhang, Qifei Zhejiang Univ Sch Software Technol Ningbo Peoples R China

With the problems of data sharing and information diddling in the field of education, we construct a highly available education consortium blockchain platform to ensure trusted sharing and privacy protection of education data. We employ erasure codes to process blockchain ledger files and optimize the data storage model according to the characteristics of education data, which can reduce the storage volume effectively. A HotStuff consensus algorithm is designed to access the ordering service of Hyperledger Fabric. A suitable educational blockchain network architecture based on the node complexity of education scenarios is proposed to achieve the high availability of the platform. To manage the education blockchain network, we implement the Fabric deployment based on Kubernetes and achieve the goal of including chaincode into Kubernetes environmental management. To improve the resource utilization of chaincode, we explore the new way of chaincode management by the functional computing service. Finally, on the premise of ensuring a 1/2 fault tolerance rate, the total ledger has decreased by 53.56%. Our platform enhanced the Byzantine fault tolerance while ensuring higher efficiency. Experimental results show that our platform is quite suitable for education scenario with many nodes.

关键词： blockchain consensus algorithm erasure codes Hyperledger Fabric serverless function computing

An Analysis under a Unified Formulation of Learning algorithms with Output Constraints

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Song, Mooho Lee, Jay-Yoon Seoul National University Korea Republic of

Neural networks (NN) excel in diverse tasks but can produce nonsensical results due to their exclusive reliance on (input, output) pairs, often conflicting with human knowledge. Injecting human knowledge via output constraints can enhance performance and reduce violations. Despite attempts to compare existing algorithms, no unified categorization of learning algorithms with output constraints exists. Our contributions are: (1) We categorize previous studies using three axes: type of constraint loss (e.g., probabilistic soft logic, REINFORCE), exploration strategy of constraint-violating examples, and integration mechanism for balancing the main task and constraints learning signals. (2) We propose new algorithms inspired by continual-learning for integrating main task and constraint information. (3) We introduce the Hβ-score metric to simultaneously evaluate main task performance and constraint violation. Our experiments on NLP tasks (NLI, STE, SRL) show that our projection-based integration mechanism outperforms others. Sampling strategy is crucial for high Hβ-scores, with better results as sample numbers increase. Additionally, soft-type constraint loss performs well when combined with sampling strategies. These insights highlight key factors for achieving high Hβ-scores and demonstrate the efficacy of our methods. © 2024, CC BY.

关键词： consensus algorithm

ON SEQUENTIAL GREEDY-TYPE BASES

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Berasategui, Miguel Berná, Pablo M. Chu, Hung Viet IMAS - UBA - CONICET - PAB I FACULTAD DE CIENCIAS EXACTAS Y NATURALES UNIVERSIDAD DE BUENOS AIRES 1428 Buenos Aires Argentina DEPARTAMENTO DE MATEMÁTICAS CUNEF UNIVERSIDAD Madrid28040 Spain DEPARTMENT OF MATHEMATICS TEXAS A&M UNIVERSITY TX77843 United States

It is known that a basis is almost greedy if and only if the thresholding greedy algorithm gives essentially the smallest error term compared to errors from projections onto intervals or in other words, consecutive terms of N. In this paper, we fix a sequence (an)∞n=1 and compare the TGA against projections onto consecutive terms of the sequence and its shifts. We call the corresponding greedy-type condition the F(an)-almost greedy property. Our first result shows that the F(an)-almost greedy property is equivalent to the classical almost greedy property if and only if (an)∞n=1 is bounded. Then we establish an analog of the result for the strong partially greedy property. Finally, we show that under a certain projection rule and conditions on the sequence (an)∞n=1, we obtain a greedy-type condition that lies strictly between the almost greedy and strong partially greedy *** Codes 41A65, 46B15 Copyright © 2023, The Authors. All rights reserved.

关键词： consensus algorithm

On a family of universal cycles for multi-dimensional permutations

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Kitaev, Sergey Qiu, Dun Department of Mathematics and Statistics University of Strathclyde 26 Richmond Street GlasgowG1 1XH United Kingdom Center for Combinatorics LPMC Nankai University Tianjin300071 China

A universal cycle (u-cycle) for permutations of length n is a cyclic word, any size n window of which is order-isomorphic to exactly one permutation of length n, and all permutations of length n are covered. It is known that u-cycles for permutations exist, and they have been considered in the literature in several papers from different points of view. In this paper, we show how to construct a family of u-cycles for multi-dimensional permutations, which is based on applying an appropriate greedy algorithm. Our construction is a generalisation of the greedy way by Gao et al. to construct u-cycles for permutations. We also note the existence of u-cycles for d-dimensional matrices. © 2024, CC BY.

关键词： consensus algorithm

ARE TWO H-SPACES HOMOTOPY EQUIVALENT? AN algorithmIC VIEW POINT

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Šimková, Mária DEPARTMENT OF MATHEMATICS AND STATISTICS MASARYK UNIVERSITY KOTLÁŘSKÁ 2 Brno611 37 Czech Republic

This paper proposes an algorithm that decides if two simply connected spaces represented by finite simplicial sets of finite k-type and finite dimension d are homotopy equivalent. If the spaces are homotopy equivalent, the algorithm finds a homotopy equivalence between their Postnikov stages in dimension d. As a consequence, we get an algorithm deciding if two spaces represented by finite simplicial sets are stably homotopy equivalent. Copyright © 2022, The Authors. All rights reserved.

关键词： consensus algorithm

HOT: An Efficient Halpern Accelerating algorithm for Optimal Transport Problems

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Zhang, Guojun Gu, Zhexuan Yuan, Yancheng Sun, Defeng The Hong Kong Polytechnic University Hong Kong

This paper proposes an efficient HOT algorithm for solving the optimal transport (OT) problems with finite supports. We particularly focus on an efficient implementation of the HOT algorithm for the case where the supports are in R2 with ground distances calculated by L22-norm. Specifically, we design a Halpern accelerating algorithm to solve the equivalent reduced model of the discrete OT problem. Moreover, we derive a novel procedure to solve the involved linear systems in the HOT algorithm in linear time complexity. Consequently, we can obtain an Ε-approximate solution to the optimal transport problem with M supports in O(M1.5/Ε) flops, which significantly improves the best-known computational complexity. We further propose an efficient procedure to recover an optimal transport plan for the original OT problem based on a solution to the reduced model, thereby overcoming the limitations of the reduced OT model in applications that require the transport map. We implement the HOT algorithm in PyTorch and extensive numerical results show the superior performance of the HOT algorithm compared to existing state-of-the-art algorithms for solving the OT problems. Copyright © 2024, The Authors. All rights reserved.

关键词： consensus algorithm

An algorithm for a Variation of the Shortest Common Superstring Problem

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Gilfanov, Arthur Boulder CO United States

This study develops an algorithm to solve a variation of the Shortest Common Superstring (SCS) problem. There are two modifications to the base SCS problem. First, one string in the set S is allowed to have up to K mistakes, defined as not matching the SCS in at most K positions. Second, no string in S can be a substring of another in S. The algorithm proposed for the problem is *** Codes F.2.2 © 2024, CC BY.

关键词： consensus algorithm

学校读者我要写书评

暂无评论

Exact Exploration

arXiv 2024年

作者： Blass, Andreas Dershowitz, Nachum Gurevich, Yuri Math Dept University of Michigan Ann ArborMI United States School of Computer Science Tel Aviv University Israel Microsoft Research RedmondWA98052 United States

Recent analysis of classical algorithms resulted in their axiomatization as transition systems satisfying some simple postulates, and in the formulation of the Abstract State Machine Theorem, which assures us that any classical algorithm can be emulated step-by-step by a most general model of computation, called an "abstract state machine". We refine that analysis to take details of intra-step behavior into account, and show that there is in fact an abstract state machine that not only has the same state transitions as does a given algorithm but also performs the exact same tests on states when determining how to proceed to the next state. This enhancement allows the inclusion—within the abstract-state-machine framework—of algorithms whose states only have partially-defined equality, or employ other native partial functions, as is the case, for instance, with inversion of a matrix of computable reals. Copyright © 2024, The Authors. All rights reserved.

关键词： consensus algorithm