Self-Organization and Complexity in Bio-Inspired Neural Networks During Learning Processes

The brain is the perfect prototype of a complex system. Over the past decades, researchers have increasingly borrowed tools and concepts from the field of complexity to make sense of how the brain works, applying these approaches to both theoretical models and experimental data. Notably, complex network analyses have also found applications in Artificial Intelligence (AI) research, as learning modifies the system's topological properties. However, in biological neural networks, time also plays a crucial role in their functioning. Due to their intrinsic spiking nature, they can be studied through the lens of systems exhibiting intermittent complex behaviour. The theoretical framework of Temporal Complexity (TC), also known as Intermittency-Driven Complexity (IDC), captures these intermittent dynamics by analyzing the metastability of neural states emerging from nonlinear neuronal interactions. TC is distinguished by power-law decay in inter-event times or by scaling properties within an event-driven diffusion process. This thesis presents findings from a comprehensive investigation into how TC scaling indexes behave across various neural network models under learning paradigm. In the first part, I investigated a bio-inspired Hopfield-type model to explore how different connectivity topologies, specifically random and scale-free networks, shape network dynamics. This is motivated by the fact that learning modifies network topology, and it is therefore interesting to understand how different topological configurations give rise to different temporal patterns. Beyond this, I examined specific dynamic patterns that emerge in these networks, analyzing their stability by tracking changes in TC indices. Surprisingly, similar activity patterns were found in both random and scale-free networks. Particularly, both topologies exhibited power-law decays in the activity distribution, a hallmark of emergent self-organizing complex behavior. The study revealed that in scale-free networks, this power-law behavior manifests at lower noise levels compared to random networks. The second part of my project focused on evaluating TC indices in a model capable of storing different complex patterns using an associative memory learning method, characteristic of biological neural networks. The model studied was a Dense Associative Memory (DAM) model with an exponential interaction function and multiplicative random noise. By analyzing the overlap parameter, I found that the system transitions into a critical region of the noise level that depends on the number of stored patterns. The critical state corresponds to a maximum degree of self-organization present in the network's activity, as highlighted by the emergence of long-range temporal correlations. Finally, I moved to a fully biological framework by implementing an Izhikevich spiking neural model with Spike-Timing-Dependent Plasticity (STDP) as the learning mechanism. This allowed me to evaluate how TC indices respond when the network processes different input patterns. I compared these indices between networks with and without active learning, revealing that plasticity influences the temporal complexity of neural avalanches.