基于最优控制的分层自适应方法，提升神经ODE的分类性能
Layerwise goal-oriented adaptivity for neural ODEs: an optimal control perspective
- 从最优控制视角设计分层自适应机制，优化神经ODE参数
- 在多个经典数据集上实现更高分类准确率，验证方法有效性
- 适合对神经微分方程建模与优化感兴趣的科研人员
本文提出一种新型的神经网络架构分层自适应构造方法。该方法基于神经微分方程最优控制中的目标导向双加权残差技术，构建了一个以系数为控制变量、特定损失函数为目标的常微分方程约束优化问题。我们基于神经ODE的DG(0)伽辽金离散化，采用显式欧拉时间推进方案实现该方法。优化问题通过Adam算法与适配于正则化项诱导的H¹拓扑的BFGS方法求解。最后，我们将该方法应用于数据集分类任务，在若干文献中知名实例上展示了实验结果。
原文摘要 · Abstract (English)
In this work, we propose a novel layerwise adaptive construction method for neural network architectures. Our approach is based on a goal--oriented dual-weighted residual technique for the optimal control of neural differential equations. This leads to an ordinary differential equation constrained optimization problem with controls acting as coefficients and a specific loss function. We implement our approach on the basis of a DG(0) Galerkin discretization of the neural ODE, leading to an explicit Euler time marching scheme. The resulting optimization problem is solved using the Adam algorithm and a BFGS method adapted to the $H^1$ topology induced by the regularization term. Finally, we apply our method to the construction of neural networks for the classification of data sets, where we present results for a selection of well known examples from the literature.
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