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.

翻译：本文探讨了将丢番图方程融入神经网络架构以提升模型可解释性、稳定性和效率的方法。通过将神经网络参数编码为丢番图方程的整数解并进行解码，我们提出了一种新颖的途径，能够同时提升深度学习模型的精度与鲁棒性。该方法在训练过程中通过定制损失函数强制施加丢番图约束，从而实现了更好的泛化性能、更小的误差界以及更强的对抗攻击抵御能力。我们在图像分类和自然语言处理等多个任务中验证了该方法的有效性，均观察到模型在准确率、收敛性和鲁棒性方面的提升。本研究为融合数学理论与机器学习以构建更具可解释性和高效性的模型提供了新的视角。