Universal Approximation and Learning of Trajectories Using Oscillators

Natural and artificial neural circuits must be capable of traversing specificstate space trajectories. A natural approach to this problem is to learn the relevant trajectories from examples. Unfortunately, gradientdescent learning of complex trajectories in amorphous networks is unsuccessful. We suggest a possible approach wheretrajectories are realized by combining simple oscillators, in various modular ways. We contrast two regimes of fast and slow oscillations.