Self-organization of high-dimensional geometry of neural activity in culture

A vast number of neurons exhibit high-dimensional coordination for brain computation, both in processing sensory input and in generating spontaneous activity without external stimuli. Recent advancements in large-scale recordings have revealed that this high-dimensional population activity exhibits a scale-free structure, characterized by power law and distinct spatial patterns in principal components (PCs). However, the mechanisms underlying the formation of this high-dimensional neural coordination remain poorly understood. Specifically, it is unclear whether the characteristic high-dimensional structure of population activity emerges through self-organization or is shaped by the learning of sensory stimuli in animals. To address this question and clearly differentiate between these two possibilities, we investigated large-scale neural activity in dissociated neuronal culture using high-density multi-electrode arrays. Our findings demonstrate that the high-dimensional structure of neural activity self-organizes during network development in the absence of explicit sensory stimuli provided to animals. As the cultures mature, the PC variance exhibits a power-law decay, and the spatial structures of PCs transition from global to localized patterns, driven by the temporal correlations of neural activity. Furthermore, we observed an unexpected co-occurrence between the power-law decay in PCA and neuronal avalanches, suggesting a link between self-organized criticality and high-dimensional activity. Using a recurrent neural network model, we show that both phenomena can arise from biologically plausible heavy-tailed synaptic connectivity. By highlighting a developmental origin of the high-dimensional structure of neural activity, these findings deepen our understanding of how coordinated neural computations are achieved in the brain.