  We derive a nonlinear integro-differential transport equation describing
collective evolution of weights under gradient descent in large-width
neural-network-like models. We characterize stationary points of the evolution
and analyze several scenarios where the transport equation can be solved
approximately. We test our general method in the special case of linear
free-knot splines, and find good agreement between theory and experiment in
observations of global optima, stability of stationary points, and convergence
rates.
