The science of complexity versus artificial intelligence

This seminar explores the deep correspondence between the science of complexity and artificial intelligence (AI), tracing their historical and conceptual interplay. We begin by examining how early models of collective behavior in physics, such as the Ising model, laid the groundwork for understanding emergent computation and learning in large systems. Building upon this foundation, we revisit the Hopfield associative networks, which translated statistical mechanics principles into models of memory and pattern recognition. These developments established a bridge between complex adaptive systems and neural computation, emphasizing self-organization and attractor dynamics. As AI evolved, these ideas scaled up spectacularly, culminating in the Large Language Models (LLMs) that dominate current research. LLMs, with parameter counts of the order of 10^{^12}, embody the same tension between order and chaos characteristic of complex systems. The seminar discusses how linguistic laws — such as Zipf’s and Heaps’ laws as well as the recently descovered orderly patterns of punctuation — offer a potential pathway to manage model complexity more efficiently by exploiting the statistical regularities of language. This correspondence highlights that intelligence, whether natural or artificial, arises from structured complexity rather than sheer scale. Ultimately, the talk argues for a complexity - informed AI paradigm, where principles from physics, linguistics, and information theory converge to yield more interpretable, efficient, and human-aligned systems.