Deep one-gate per layer networks with skip connections are universal classifiers

Raul Rojas Department of Mathemanullcs and Stanullsnullcs University of Nevada Reno October 2025 Abstract This paper shows how a mulnulllayer perceptron with two hidden layers, which has been designed to classify two classes of data points, can easily be transformed into a deep neural network with one - gate layers and skip connecnullons. As shown in [1], deep one - gate per layer networks can perfectly separate points belonging to two classes in an n - dimensional space. Here, I present an alternanullve proof that may be easier to understand. This proof shows that classical neural networks that separate two classes can be transformed into deep one - gate - per - layer networks with skip connecnullons. A perceptron receives a vector input and divides input space into two subspaces: the posinullve and neganullve half - spaces (Figure 1a).