Stable Attractors Multiplicity in Disordered Neural Models

A new study demonstrates how large-deviation statistics can estimate the number of stable fixed points in neural ordinary differential equations used for computational tasks. The researchers developed a perturbative method based on disorder amplitude. For moderate coupling strengths, no qualitative differences were found between symmetric gradient dynamics and asymmetric cases where limit cycles or chaos may occur. The model was chosen for pedagogical reasons, but the approach is expected to generalize to other many-degree-of-freedom dynamical systems with random coupling matrices.