Training Neural Networks using SAT solvers

TL;DR

This paper introduces a novel algorithm that uses SAT solvers for global optimization in neural network training, aiming to overcome local optima issues faced by gradient-based methods in specific tasks.

Contribution

It presents a new approach combining SAT solvers with neural network training, demonstrating effectiveness on certain problems like parity learning.

Findings

Outperforms ADAM in parity learning tasks

Less effective than gradient methods on MNIST

Highlights scalability challenges with SAT solvers

Abstract

We propose an algorithm to explore the global optimization method, using SAT solvers, for training a neural net. Deep Neural Networks have achieved great feats in tasks like-image recognition, speech recognition, etc. Much of their success can be attributed to the gradient-based optimisation methods, which scale well to huge datasets while still giving solutions, better than any other existing methods. However, there exist learning problems like the parity function and the Fast Fourier Transform, where a neural network using gradient-based optimisation algorithm can not capture the underlying structure of the learning task properly. Thus, exploring global optimisation methods is of utmost interest as the gradient-based methods get stuck in local optima. In the experiments, we demonstrate the effectiveness of our algorithm against the ADAM optimiser in certain tasks like parity learning. However, in the case of image classification on the MNIST Dataset, the performance of our algorithm was less than satisfactory. We further discuss the role of the size of the training dataset and the hyper-parameter settings in keeping things scalable for a SAT solver.