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Previous literature offers limited clues on how to learn a periodic functionusing modern neural networks. We start with a study of the extrapolationproperties of neural networks; we prove and demonstrate experimentally that thestandard activations functions, such as ReLU, tanh, sigmoid, along with theirvariants, all fail to learn to extrapolate simple periodic functions. Wehypothesize that this is due to their lack of a "periodic" inductive bias. As afix of this problem, we propose a new activation, namely, $x + \sin^2(x)$,which achieves the desired periodic inductive bias to learn a periodic functionwhile maintaining a favorable optimization property of the ReLU-basedactivations. Experimentally, we apply the proposed method to temperature andfinancial data prediction.

Neural Networks Fail to Learn Periodic Functions and How to Fix It