Convexity lies in the eye of beholder. A note on how nonlinear optimal control problems can be given a convex formulation using the continuity equation. https://hackmd.io/@TAzH1D5uSQO0ozb_mg0NRw/r1KEH2cNkg #controltheory

Switching between two flows of a skinny neural ODE (blue and red) produces the behavior of a time-averaged thick neural ODE (green).

Averaging theory in dynamical systems has found interesting applications from stable inverted pendulums to undulating snakes and flapping wings of humming birds. Turns out there is also a lot of averaging theory behind approximation properties of neural networks. A note: https://hackmd.io/hkIgH3ZJRjyuxVEfTrwxpg