The use of parabola and its branches as a nonlinearity expanding the logical capabilities of artificial neurons is considered. In particular, the applicability of parabola branches for constructing an s-shaped function suitable for tuning a neural network by reverse error propagation is determined. The implementation of the XOR function on two and three neurons using the proposed approach is demonstrated. The main advantage of the parabola over the sigmoid is a simpler implementation, which speeds up the work of artificial neural networks.
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Хачумов М. В., Емельянова Ю. Г. Парабола как функция активации искусственных нейронных сетей // Искусственный интеллект и принятие решений, №2, 2023, с. 89–97.