Collaborative Research: Network Control Systems Science for Graph Machine Learning

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 to solve 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.