Optimizing Neural Network Performance and Interpretability with Diophantine Equation Encoding

Abstract

This paper explores the integration of Diophantine equations into neural network (NN) architectures to improve model interpretability, stability, and efficiency. By encoding and decoding neural network parameters as integer solutions to Diophantine equations, we introduce a novel approach that enhances both the precision and robustness of deep learning models. Our method integrates a custom loss function that enforces Diophantine constraints during training, leading to better generalization, reduced error bounds, and enhanced resilience against adversarial attacks. We demonstrate the efficacy of this approach through several tasks, including image classification and natural language processing, where improvements in accuracy, convergence, and robustness are observed. This study offers a new perspective on combining mathematical theory and machine learning to create more interpretable and efficient models.