Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes

Abstract Cascades over networks (e.g., neuronal avalanches, social contagions, and system failures) often involve higher-order dependencies, yet theory development has largely focused on pairwise-interaction models. Here, we develop a ‘simplicial threshold model’ (STM) for cascades simplicial complexes that encode dyadic, triadic interactions. Focusing small-world models containing both short- long-range k -simplices, explore spatio-temporal patterns manifest as frustration between local nonlocal propagations. We show interactions nonlinear thresholding coordinate to robustly guide along -dimensional generalization of paths call ‘geometrical channels’. also find this coordination enhance the diversity efficiency simplicial-complex model network, or ‘neuronal complex’. support these findings with bifurcation data-driven approaches based latent geometry. Our provide fruitful directions uncovering multiscale, multidimensional mechanisms orchestrate cascades.