This paper demonstrates that a single-layer neural network using Parametric Rectified Linear Unit (PReLU) activation can solve the XOR problem, a simple fact that has been overlooked so far. We compare this solution to the multi-layer perceptron (MLP) and the Growing Cosine Unit (GCU) activation function and explain why PReLU enables this capability. Our results show that the single-layer PReLU network can achieve 100\% success rate in a wider range of learning rates while using only three learnable parameters.
@article{arxiv.2409.10821,
title = {PReLU: Yet Another Single-Layer Solution to the XOR Problem},
author = {Rafael C. Pinto and Anderson R. Tavares},
journal= {arXiv preprint arXiv:2409.10821},
year = {2024}
}