XOR_p A maximally intertwined p-classes problem used as a benchmark with built-in truth for neural networks gradient descent optimization
This provides a new benchmark with built-in truth for evaluating gradient descent optimizers in neural networks, though it is incremental as it builds on existing XOR problems.
The authors tackled the XOR_p problem, a p-class generalization of XOR, by solving it with a single hidden layer network and testing various optimizers and activation functions. They found that Adam optimizer with ELU activation converged most often and fastest to perfect classification, achieving results up to p=191.
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.