Collaborative Research: CIF: Small: A New Paradigm for Distributed Information Processing, Simulation and Inference in Networks: The Promise of Law of Small Numbers

以可靠、高效和安全的方式访问、处理和存储分布式数据的能力已经成为日常生活中不可或缺的一部分。各种新兴应用，如增强现实、自动驾驶汽车和云计算，都严重依赖于处理大量分布式信息。疫情进一步凸显了全球对技术的需求，使通信、协作、教育和科学讨论能够在保持物理距离的同时进行，这提高了人们对通信网络基础设施重要性的认识。对更快的数据处理和更高的通信速率的指数增长的需求提出了新的挑战。该项目通过开发分布式信息处理、随机性生成、数据存储和传输以及推理的新方法和技术来解决这些挑战。该项目将紧密结合研究与一个重要的教育和推广计划，包括两个重点领域：（i）培训学生进行跨学科研究，（ii）广泛传播新课程开发和学生参与的形式的研究成果。将作出协调一致的努力，扩大妇女和代表人数不足的少数民族学生对该项目的参与。该项目基于两个研究方向，预计将提供对管理信息处理的基本规律的更深入理解。在第一个推力，一个新的框架开发的基础上两个概念的创新：（一）一个表征的基本记忆结构的信息处理功能，使用一个新的概念的依赖谱，及（ii）发展一个新的法律的小数，它描述了一个基本的依赖谱和分布式合作之间的相互作用。特别是，该项目揭示了分布式信息处理功能的相关性保持能力（这是分布式合作所必需的）与其有效执行单个信息处理任务的能力之间的权衡。第二个重点解决了两个应用场景。(i)建立在依赖频谱的概念上，开发了用于分布式数据压缩以及在干扰和广播网络中传输信息的新技术。(ii)推导了分布式随机数生成算法的基本限制和实用设计。这些创新在渐近性能极限的表征和建设性的实用算法方面都取得了显著的进步。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The ability to access, process, and store distributed data in a reliable, efficient, and secure manner has become indispensable in everyday lives. A variety of emerging applications such as augmented reality, autonomous vehicles, and cloud computing heavily rely on handling large amounts of distributed information. The pandemic has further accentuated the global need for technologies that enable communication, collaboration, education and scientific discourse whilst maintaining physical distance, and this has increased awareness of the critical nature of the communication network infrastructure. The exponentially increasing demands for faster data processing and higher communication rates pose new challenges. This project addresses these challenges by developing novel approaches and techniques for distributed information processing, randomness generation, data storage and transmission, and inference. The project will tightly integrate research with a significant education and outreach program consisting of two focus areas: (i) Training students in interdisciplinary research, and (ii) Broadly disseminating research outcomes in the forms of new curricular development and student involvement. A concerted effort will be made to broaden the participation of women and under-represented minority students in the project. The project is based on two research thrusts that are expected to provide a deeper understanding of the fundamental laws that govern the processing of information. In the first thrust, a new framework is developed based on two conceptual innovations: (i) A characterization of the fundamental memory structure of information processing functions using a novel notion of dependency spectrum, and (ii) Development of a new law of small numbers, which describes a fundamental interplay between the dependency spectrum and distributed cooperation. In particular, the project uncovers a trade-off between the correlation-preserving ability of distributed information-processing functions --- which is necessary for distributed cooperation --- and their ability to efficiently perform individual information-processing tasks. The second thrust addresses two application scenarios. (i) Building upon the concept of dependency spectrum, novel techniques are developed for distributed data compression, and transmission of information in interference and broadcast networks. (ii) The fundamental limits and practical design of distributed randomness generation algorithms are derived. These innovations lead to significant improvements over the state of the art both in terms of characterizations of asymptotic performance limits and constructive practical algorithms.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.