Robust Classification Using Contractive Hamiltonian Neural ODEs

Deep neural networks can be fragile and sensitive to small input perturbations that might cause a significant change in the output. In this letter, we employ contraction theory improve robustness of ODEs (NODEs). A dynamical system is contractive if all solutions with different initial conditions converge each other exponentially fast. As consequence, become less relevant over time. Since NODEs data corresponds condition systems, show contractivity mitigate effect perturbations. More precisely, inspired by Hamiltonian dynamics, propose class (CH-NODEs). By properly tuning scalar parameter, CH-NODEs ensure design trained using standard backpropagation. Moreover, enjoy built-in guarantees non-exploding gradients, which well-posed training process. Finally, demonstrate on MNIST image classification problem noisy test data.