CAREER: Learning from Data on Structured Complexes: Products, Bundles, and Limits

职业：从结构化复合体的数据中学习：乘积、捆绑和限制

• 批准号: 2340481
• 负责人: Santiago Segarra
• 金额: $ 59.91万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-04-01 至 2029-03-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2340481&HistoricalAwards=false
• 关键词: CAREER; Learning; Data; Structured; Complexes

Artificial intelligence (AI) has shown impressive performance in a variety of tasks involving data in the form of text, audio, and images, such as face recognition and text summarization. However, data from many fields of knowledge can be naturally defined over less conventional domains, such as climate data defined on spheres (representing the Earth) and traffic data defined on road networks. Consequently, over the past few years, AI has been extended to these settings, oftentimes by representing these domains as graphs. However, AI tools designed to be implemented in any graph necessarily disregard the structure of specific graphs of interest. For example, traffic data that changes over time can be represented on a structured graph that combines the underlying road network with the linear evolution of time. Motivated by this view, the investigators will focus on classes of graphs whose additional structural properties are both practically relevant (i.e., they represent real-world data domains) and methodologically advantageous (i.e., they can be exploited to better learn from data). More broadly, this project will aim to boost the utility of AI by leveraging structural properties often found in real-world data. The research will be integrated into educational activities by development of courses and teaching modules for high school, undergraduate, and graduate students and includes broadening participation activities with students of Latin American origin. The primary research goal of this project is to develop a principled theory to process and learn from data defined on structured (higher-order) networks. In particular, the investigators will focus on three types of structures for graphs and (simplicial and cell) complexes. First, product complexes will be considered, where the data domain can be decomposed as the product of two (or more) constituent simpler domains. By specializing discrete Hodge theory to this data structure, novel neural architectures with transferability guarantees will be derived. Second, graph bundles will be studied, which are not globally decomposable but present a local product-like structure. In this case, the focus will be to improve data representation by designing signal processing transformations that can naturally handle the non-orientable nature of bundles. Lastly, the researchers will analyze the limits of simplicial complexes as the number of nodes grows. The objective here is to leverage the regularity of these limiting objects to efficiently design neural architectures for large-scale relational domains. From a theoretical standpoint, this project uniquely combines concepts from graph theory, algebraic topology, signal processing, deep learning, and linear integral operators to derive a fundamental understanding of learning in structured domains.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.

人工智能（AI）在涉及文本、音频和图像形式的数据的各种任务中表现出令人印象深刻的性能，例如人脸识别和文本摘要。然而，来自许多知识领域的数据可以自然地在不太传统的领域上定义，例如在球体（代表地球）上定义的气候数据和在道路网络上定义的交通数据。因此，在过去的几年里，人工智能已经扩展到这些设置，通常通过将这些域表示为图形。然而，设计用于在任何图中实现的AI工具必然会忽略感兴趣的特定图的结构。例如，随时间变化的交通数据可以在结构化图上表示，该结构化图将基础道路网络与时间的线性演变相结合。受此观点的启发，研究人员将专注于其附加结构属性都是实际相关的图的类别（即，它们代表真实世界的数据域）和方法上的优势（即，它们可以被利用来更好地从数据中学习）。更广泛地说，该项目旨在通过利用现实世界数据中常见的结构属性来提高人工智能的实用性。 这项研究将通过为高中、本科和研究生制定课程和教学模块，纳入教育活动，包括扩大拉丁美洲裔学生的参与活动。 该项目的主要研究目标是开发一种原则性的理论来处理和学习结构化（高阶）网络上定义的数据。特别是，研究人员将集中在三种类型的结构图和（单纯和细胞）复杂。首先，将考虑乘积复合体，其中数据域可以被分解为两个（或更多个）组成较简单域的乘积。通过专门的离散霍奇理论，这种数据结构，新的神经结构与可转移性的保证将派生。第二，研究图丛，它不是全局可分解的，但呈现局部乘积结构。在这种情况下，重点将是通过设计可以自然处理束的不可定向性质的信号处理转换来改进数据表示。最后，研究人员将分析单纯复形随着节点数量增长的极限。这里的目标是利用这些限制对象的规律性来有效地设计大规模关系域的神经架构。从理论的角度来看，该项目独特地结合了图论、代数拓扑、信号处理、深度学习和线性积分算子的概念，以获得对结构化领域学习的基本理解。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。