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

arXiv: https://arxiv.org/abs/2409.10821 · HTML: https://mlsanity.com/paper/2409.10821/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 12 references that are in the map.
- First posted on arXiv 17 Sep 2024.

## Builds on (most cited first, 6 of 6)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Three Decades of Activations: A Comprehensive Survey of 400 Activation Functions for Neural Networks](https://mlsanity.com/paper/2402.09092/) (2024)
- [Layer Folding: Neural Network Depth Reduction using Activation Linearization](https://mlsanity.com/paper/2106.09309/) (2021)
- [Growing Cosine Unit: A Novel Oscillatory Activation Function That Can Speedup Training and Reduce Parameters in Convolutional Neural Networks](https://mlsanity.com/paper/2108.12943/) (2021)
- [A brief history of AI: how to prevent another winter (a critical review)](https://mlsanity.com/paper/2109.01517/) (2021)

## Built on by (most cited first, 3 of 3)

- [AGTCNet: A Graph-Temporal Approach for Principled Motor Imagery EEG Classification](https://mlsanity.com/paper/2506.21338/) (2025)
- [Neuroevolution of Self-Attention Over Proto-Objects](https://mlsanity.com/paper/2505.00186/) (2025)
- [A nonparametric two-sample test using a parametric integral probability metric](https://mlsanity.com/paper/2606.16941/) (2026)

## Abstract (arXiv)

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.