# XOR_p A maximally intertwined p-classes problem used as a benchmark with built-in truth for neural networks gradient descent optimization

## TL;DR

This paper introduces a generalized XOR problem for p classes, serving as a challenging benchmark for neural network optimization, and finds that Adam with ELU performs best across various prime p values.

## Contribution

It presents a new p-classes XOR generalization as a benchmark and evaluates optimizer and activation function performance on it.

## Key findings

- Adam with ELU converges most often and fastest.
- The problem landscape is intricate despite simplicity.
- Effective for testing gradient descent algorithms.

## Abstract

A natural p-classes generalization of the eXclusive OR problem, the subtraction modulo p, where p is prime, is presented and solved using a single fully connected hidden layer with p-neurons. Although the problem is very simple, the landscape is intricate and challenging and represents an interesting benchmark for gradient descent optimization algorithms. Testing 9 optimizers and 9 activation functions up to p = 191, the method converging most often and the fastest to a perfect classification is the Adam optimizer combined with the ELU activation function.