This paper presents the Standalone Neural ODE (sNODE), a continuous-depth neural ODE model capable of describing a full deep neural network. This uses a novel nonlinear conjugate gradient (NCG) descent optimization scheme for training, where the Sobolev gradient can be incorporated to improve smoothness of model weights. We also present a general formulation of the neural sensitivity problem and show how it is used in the NCG training. The sensitivity analysis provides a reliable measure of uncertainty propagation throughout a network, and can be used to study model robustness and to generate adversarial attacks. Our evaluations demonstrate that our novel formulations lead to increased robustness and performance as compared to ResNet models, and that it opens up for new opportunities for designing and developing machine learning with improved explainability.

翻译：本文介绍了独立神经值(sNODE),这是一个连续深入的神经值(sNODE)模型,能够描述一个完整的深神经网络。它使用一种新的非线性共振梯度(NCG)血统优化培训计划,可以将Sobolev梯度纳入其中,以提高模型重量的平滑性。我们还提供了神经灵敏度问题的一般表述,并展示了NCG培训中如何使用它。敏感性分析为整个网络的不确定性传播提供了可靠的衡量标准,并可用于研究模型坚固性并产生对抗性攻击。我们的评估表明,我们的新配方与ResNet模型相比,其性能和性能都提高了,并且为设计和开发机器学习提供了新的机会,并改进了解释性。