The universal approximation Theorem 3.1 immediately implies another universal approximation Thus y (t) solves the ODE (2.6), with initial condition y (0) = y (0) = 0 . Reconstruction of a continuous signal from its sine transform. Step 0: (Equicontinuity) We recall the following fact from topology. F (τ):= null f (τ), for τ 0, f ( τ), for τ 0. Since F is odd, the Fourier transform of F is given by We provide the details below. The next step in the proof of the fundamental Lemma 3.5 needs the following preliminary result in By (B.3), this implies that It follows from Lemma 3.4 that for any input By the sine transform reconstruction Lemma B.1, there exists It follows from Lemma 3.6, that there exists Indeed, Lemma 3.7 shows that time-delays of any given input signal can be approximated with any Step 1: By the Fundamental Lemma 3.5, there exist It follows from Lemma 3.6, that there exists an oscillator Step 3: Finally, by Lemma 3.8, there exists an oscillator network,

Given this wide prevalence of (networks of) oscillators in nature and man-made devices, it is not surprising that oscillators have inspired various machine learning architectures in recent years.

Implicitly or explicitly, this data is composed of domains--varying distributions of language.

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The setting described is summarized in Box A.

Work done while visiting Harvard University.

Section C describes the details of the experimental setup, including network architectures, hyperparameters,andhardwaredetails. Thisoutcomeemphasizes the necessity of feature interaction or feature fusion to tackle intricate situations. Furthermore, an amalgamation of feature fusion and value fusion can offer better performance. This adjustment allows us to evaluate the robustness and adaptability of our approach in handling a larger number of vehicles in the environment. As we increase the number of vehicles on the road, Fig. A2 (a) clearly indicates that HAVE consistently delivers the highest performance. The training and testing curves of HAVE and other comparable methods are given in A4.