Paon: A New Neuron Model Using Padé Approximants

Convolutional neural networks (CNN) are built upon the classical McCulloch-Pitts neuron model, which is essentially a linear model, where the nonlinearity is provided by a separate activation function. Several researchers have proposed enhanced neuron models, including quadratic neurons, generalized operational neurons, generative neurons, and super neurons, with stronger nonlinearity than that provided by the pointwise activation function. There has also been a proposal to use Padé approximation as a generalized activation function. In this paper, we introduce a brand new neuron model called Padé neurons (Paons <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>), inspired by the Padé approximants, which is the best mathematical approximation of a transcendental function as a ratio of polynomials with different orders. We show that Paons are a super set of all other proposed neuron models. Hence, the basic neuron in any known CNN model can be replaced by Paons. In this paper, we extend the well-known ResNet to PadeNet (built by Paons) to demonstrate the concept. Our experiments on the single-image super-resolution task show that PadeNets can obtain better results than competing architectures.<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>https://github.com/onur-keles/Paon