Geometric Origin of Exact Mean-Field Reductions: M{ö}bius Symmetry and the Lorentzian Ansatz

Low-dimensional descriptions of large systems of coupled oscillators and spiking neurons rely heavily on the Lorentzian Ansatz. We show that its privileged role is geometric rather than heuristic: for the transport induced by Riccati dynamics, the Cauchy-Lorentz family indeed emerges as the unique c... View More