LyaNet: A Lyapunov Framework for Training Neural ODEs

INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 162(2022)

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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 a correct prediction that minimizes the original supervised loss. Theoretically, we show that minimizing Lyapunov loss guarantees exponential convergence to a 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 is available at https://github.com/ivandariojr/LyapunovLearning.
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