Supplementary Material for: Neural Oscillators are Universal

The universal approximation Theorem 3.1 immediately implies another universal approximation Fix a time interval [0, T ] for (an arbitrary choice) T = 2. Let K Thus y(t) solves the ODE (2.6), with initial condition y(0) = ẏ(0) = 0. Reconstruction of a continuous signal from its sine transform. Let [0, T ] R be an interval. We consider the reconstruction of continuous functions u K. Step 0: (Equicontinuity) We recall the following fact from topology. We now consider the following odd extension of f to all of R: { f(τ), for τ 0, F (τ):= f( τ), for τ 0. Let ϵ > 0 be arbitrary. Our goal is to uniformly approximate F (τ) on the interval [0, t].