基于神经正切核与雷姆达赫复杂度，提出一步式早停策略。
One-Step Early Stopping Strategy using Neural Tangent Kernel Theory and Rademacher Complexity
- 利用神经正切核特征值与初始误差向量，推导最优早停时间。
- 在参数量适中的场景下，早停后模型泛化误差上界更优。
- 适用于需要稳定控制性能的机器学习系统，如物理建模任务。
早停策略通过在训练误差最小前停止神经网络（NN）的训练过程，使模型保持良好泛化能力，从而对训练集外数据做出准确预测，并获得对统计误差（“总体损失”）的良好估计。本文基于神经正切核理论与雷姆达赫复杂度，给出一种解析形式的最优停止时间估计，其核心依赖于初始训练误差向量及神经正切核的特征值。该方法在参数量相对数据量不大的欠参数化场景中表现优异。文中以模拟范德波尔振子模型预测控制（MPC）的神经网络为例进行了验证。
原文摘要 · Abstract (English)
The early stopping strategy consists in stopping the training process of a neural network (NN) on a set $S$ of input data before training error is minimal. The advantage is that the NN then retains good generalization properties, i.e. it gives good predictions on data outside $S$, and a good estimate of the statistical error (``population loss'') is obtained. We give here an analytical estimation of the optimal stopping time involving basically the initial training error vector and the eigenvalues of the ``neural tangent kernel''. This yields an upper bound on the population loss which is well-suited to the underparameterized context (where the number of parameters is moderate compared with the number of data). Our method is illustrated on the example of an NN simulating the MPC control of a Van der Pol oscillator.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。