Collaborative Research: Network Control Systems Science for Graph Machine Learning

准确和有效地表示图结构的数据对于开发能够从这些数据中学习、推理和概括的机器学习系统和模型至关重要，这些数据普遍存在于自然和工程系统中。利用现代机器学习(ML)方法来解决网络中的复杂计算任务依赖于成功地将图表示为有限维向量空间中的点。该项目提供了一种基于网络控制系统理论的新范式来有效地表示图ML的图形数据。通过将图建模为受控网络动态系统，本项目设计了具有全面优越性能的图表示，包括表现力、任务精度、可扩展性、计算开销和广泛的适用性。所提出的基于控制的方法利用了网络动态和底层图形结构之间的相互作用，使得能够设计出功能强大且富有表现力的图形表示。这是通过在节点处注入信号从外部探测网络并观察它们的响应来解码网络结构来实现的，最终导致更好的图形表示。此外，这些方法建立了使用基于控制的表示来区分图的基本性能限制和保证。所提出的研究带来了实质性的智力优势，包括基于网络控制的框架，该框架生成适合于广泛的图机器学习任务的图表示，例如图和节点分类以及链接预测。该项目探索了将基于控制的嵌入与现有方法相结合的机制，并将这些方法扩展到复杂网络，包括时变网络和基本图可区分性问题。拟议研究的直接影响是通过利用控制论方法来弥合“学习控制”方面的知识差距，并改进网络中的数据驱动学习方法。这种控制和网络学习的联盟极大地促进了网络学习和优化，具有广泛的技术、经济和社会影响。更广泛的影响是通过对研究生和本科生进行跨学科培训、广泛传播研究成果和实验数据来实现的。外展活动包括旨在准备和激励高中生和少数族裔学生从事STEM职业的研讨会。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Representing graph-structured data accurately and effectively is paramount for developing machine learning systems and models capable of learning, reasoning, and generalizing from such data, ubiquitous throughout natural and engineering systems. Utilizing modern machine learning (ML) approaches tosolve complex computational tasks in networks relies on successful graph representation as points in a finite dimensional vector space. This project offers a new paradigm grounded in networked control system theory to represent graph data for graph ML effectively. By modeling graphs as controlled networked dynamical systems, this project designs graph representations with overall superior performance, including expressiveness, task accuracy, scalability, computational overhead, and broad applicability. The proposed control-based approach leverages the interplay between network dynamics and the underlying graph structure, enabling the design of powerful and expressive graph representations. This is achieved by externally probing networks through signal injection at nodes and observing their responses to decode the network structure, ultimately leading to superior graph representations. Additionally, these methods establish fundamental performance limits and guarantees for distinguishing graphs from each other using control-based representations.The proposed research brings substantial intellectual merits, including a network control-based framework that generates graph representations suitable for a wide range of graph machine learning tasks, such as graph and node classification and link prediction. The project explores mechanisms to integrate control-based embeddings with existing approaches and extend the methods to complex networks, including time-varying networks and the fundamental graph distinguishability problem. The direct impact of the proposed research is to bridge the knowledge gaps in “control for learning” and improve data-driven learning approaches in networks by leveraging the control-theoretic methods. This alliance of control and network learning significantly advances network learning and optimization with broad technological, economic, and societal implications. The broader impacts are achieved through interdisciplinary training of graduate and undergraduate students, broad dissemination of research results, and experimental data. The outreach activities include workshops designed to prepare and inspire high school and minority students to pursue STEM careers.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.