Abstract:
Collective systems in nature and biology exhibit remarkable self-organizing capabilities, characterized by complex interactions across vast scales in both time and space. Over billions of years, these systems have proliferated and given rise to the immense diversity of life and ecology found on Earth and are now one of the most dominant properties of our planet. The success and proliferation of life on Earth is a testament to how powerful self-organizing processes can be, yet understanding even a subset of these complex living systems is an extremely challenging problem. However, living systems, and even some abiotic complex systems, share many similarities. This raises the questions as to whether there exists universal principles that underpin the diversity of complex systems observed on Earth.
The criticality hypothesis, which views collective systems through the lens of statistical physics, seeks to determine the existence of such universal properties. Originally rooted in the study of magnetism, the properties of critical phenomena, which are usually detected via power-law statistics, have also been found in a variety of biological systems. These include gene-regulatory networks, evolutionary dynamics, animal swarms, or neural activity, suggesting the propensity for living systems to operate near a critical point. These observations suggest that life and complexity may also be critical phenomena, where a growing body of work is now showing how optimal computational properties emerge near critical points. However, a gap remains between theoretical and empirical work on criticality and its application, where this dissertation aims to explore and simulate complex systems and test their relation to criticality.
In three of the publications presented, we find that systems near critical regimes offer advantages in aesthetics, evolutionary dynamics, and neural network optimality. For aesthetics, abstract images with slowly decaying autocorrelations are perceived as more pleasing. In evolutionary dynamics, we demonstrate that embodied Ising neural agents evolve faster near the critical regime but converge to sub-critical states unless task complexity increases. For neural network optimality, we show that the best-performing models on long-memory tasks have more slowly decaying autocorrelations, linked to a closeness to a critical state, and that this performance is strongly influenced by the learning curriculum used.
The remaining two publications explore adaptivity and self-organization. One paper presents methods to simulate large-scale heterogeneous cellular automata (CA), demonstrated on a plastic spiking neural network and an adaptive Ising model. For the Ising model, we show that robust self-organized criticality can be implemented by using heterogeneous and adaptive CA rules. The other paper on neural plasticity in embodied agents shows that the optimality of plasticity rules depends on environmental and task conditions, with rule specificity emerging under certain constraints.
In summary, this dissertation examines complex systems to relate function and performance in applied settings to theoretical principles. While universal properties account for much of their behavior, they are modified by specific constraints, suggesting these properties are useful initial conditions for adaptive systems, which must undergo further optimization in practical applications.
complex systems