LyaNet：一个训练神经常微分方程的李雅普诺夫框架
LyaNet: A Lyapunov Framework for Training Neural ODEs
摘要：
我们提出了一种方法，通过使用控制理论的稳定性李雅普诺夫条件训练常微分方程。我们的方法，称为LyaNet，是基于一种新的李雅普诺夫损失公式，鼓励推理动态快速收敛到正确的预测。理论上，我们表明，最小化李雅普诺夫损失保证指数收敛到正确的解决方案，并使一个新的鲁棒性保证。我们还提供了实用的算法，包括一个避免通过求解器或使用伴随方法的反向传播的成本。相对于标准的神经ODE训练，我们根据经验发现LyaNet可以提供更好的预测性能，更快的推理动态收敛，以及更好的对抗鲁棒性。我们的代码可在https://github.com/ivandariojr/LyapunovLearning上获得。
英文摘要：
We propose a method for training ordinary differential equations by using a control-theoretic Lyapunov condition for stability. Our approach, called LyaNet, is based on a novel Lyapunov loss formulation that encourages the inference dynamics to converge quickly to the correct prediction. Theoretically, we show that minimizing Lyapunov loss guarantees exponential convergence to the correct solution and enables a novel robustness guarantee. We also provide practical algorithms, including one that avoids the cost of backpropagating through a solver or using the adjoint method. Relative to standard Neural ODE training, we empirically find that LyaNet can offer improved prediction performance, faster convergence of inference dynamics, and improved adversarial robustness. Our code available at https://github.com/ivandariojr/LyapunovLearning .
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
