1210.5082 (Gilles Wainrib et al.)

Topological and Dynamical Complexity of Random Neural Networks    [PDF]

Gilles Wainrib, Jonathan Touboul

In this Letter we investigate the explosion of complexity arising near the phase transition for random neural networks. We show that the mean number of equilibria undergoes a sharp transition from one equilibrium before the phase transition, to a very large number scaling exponentially with the dimension on the system. We compute the exponential rate of divergence, called topological complexity, near criticality. Strikingly, we show that it behaves exactly like classical measures of dynamical complexity such as the Lyapunov exponent, suggesting an unexplored link between topological and dynamical complexity.

View original: http://arxiv.org/abs/1210.5082