Elucidating the Laws of Emergent Cognition and Biological Intelligence

Biological intelligence (BI) arises from complex multiscale interactions among neurons and glia that are continuously optimized for exploration and self-organization under unknown unknowns. Despite numerous efforts for understanding the structure and dynamics (collective behaviors) of complex intelligent systems, the functional mapping—the mathematical relationship linking observable neuronal and glia activity to the underlying cognitive blueprint—remains unknown. We address this challenge by developing foundamental mathematical tools to analyze dynamical and structural observations to decode the network's structural and functional laws of emergence. Toward this end, we introduce a comprehensive node-based multifractal analysis that jointly analyzes the neuronal interspike intervals (ISIs) and the rich neuronal network topologies in order to characterize the non-linear, non-stationary signatures of complex biological computation. We demonstrate that this multifractal profile functions as a robust, intrinsic measure of network topology, revealing a principle of structural invariance where the network's architectural complexity is highly sensitive to physical connectivity but surprisingly consistent across varied external stimuli. Furthermore, the profile is robustly localized and is not confounded by unobserved neuronal dynamics. Applying this framework to goal-directed spiking neural networks (SNNs), we show that multifractal analysis clearly differentiates architectures designed for diverse tasks, thereby establishing a quantifiable law of topological-functional unification. This work provides a critical step toward establishing a rigorous, quantitative framework for defining the emergent cognitive properties encoded in neuronal network structure.