Understanding Complex and Learning Systems through Structure, Scale, and Feedback

A central tenet of network science is that structure determines function: patterns of interaction shape collective behavior, robustness, and the flow of information. Networks also provide a natural language for feedback and scale, two other defining features of complex systems. In this talk, I will discuss how structure, scale, and feedback shape the function—and malfunction—of complex and learning systems through three research directions. First, I study homophily in higher-order networks. Moving from pairwise to group interactions raises new challenges for measuring and modeling homophily. I will discuss recent work on higher-order homophily and show how group-size-dependent homophily can shape inequalities in information access under nonlinear social contagion. Second, I ask how reasoning in large language models changes with scale. By treating capability and efficiency as latent properties inferred across tasks of varying difficulty, we find that reasoning capability grows sublinearly with model size, while efficiency depends only weakly on scale. Ongoing work examines whether reasoning success leaves statistical signatures in Chain-of-Thought traces, including Zipf’s law, Heaps’ law, and long-range correlations. Finally, I investigate machine-learning predictions for complex systems. I show how graph structure affects the generalization and robustness of graph-based neural ODEs, and then turn to settings in which predictions themselves reshape the system. This motivates a framework combining performative prediction, adaptive networks, and statistical physics to study the coupled evolution of networks and learning algorithms.