PReLU: Yet Another Single-Layer Solution to the XOR Problem

Anderson R. Tavares; Rafael C. Pinto

PReLU: Yet Another Single-Layer Solution to the XOR Problem

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arxiv 2409.10821 v1 pith:DCLL6VRE submitted 2024-09-17 cs.NE cs.AIcs.LG

Rafael C. Pinto , Anderson R. Tavares This is my paper · ORCID

classification cs.NEcs.AIcs.LG

keywords prelusingle-layeractivationnetworkproblemsolutionunitachieve

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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.

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