论文标题
使用收缩性哈密顿神经odes的强大分类
Robust Classification using Contractive Hamiltonian Neural ODEs
论文作者
论文摘要
深神经网络可能会脆弱，并且对小输入扰动可能会导致输出发生重大变化。在本文中，我们采用收缩理论来改善神经odes的鲁棒性（节点）。如果所有具有不同初始条件不同的解决方案彼此相互收敛，则动态系统是承包的。结果，随着时间的推移，在初始条件下的扰动变得越来越少。由于在节点中，输入数据对应于动态系统的初始条件，因此我们表明合并性可以减轻输入扰动的效果。更确切地说，受到汉密尔顿动力学的节点的启发，我们提出了一类收缩性汉密尔顿节点（CH节点）。通过正确调整标量参数，CH节点可以通过设计确保合并性，并且可以使用标准反向传播进行培训。此外，CH-Nodes享受内置的非爆炸梯度保证，这确保了良好的培训过程。最后，我们证明了与嘈杂的测试数据对MNIST图像分类问题的CH节点的鲁棒性。
Deep neural networks can be fragile and sensitive to small input perturbations that might cause a significant change in the output. In this paper, we employ contraction theory to improve the robustness of neural ODEs (NODEs). A dynamical system is contractive if all solutions with different initial conditions converge to each other exponentially fast. As a consequence, perturbations in initial conditions become less and less relevant over time. Since in NODEs the input data corresponds to the initial condition of dynamical systems, we show contractivity can mitigate the effect of input perturbations. More precisely, inspired by NODEs with Hamiltonian dynamics, we propose a class of contractive Hamiltonian NODEs (CH-NODEs). By properly tuning a scalar parameter, CH-NODEs ensure contractivity by design and can be trained using standard backpropagation. Moreover, CH-NODEs enjoy built-in guarantees of non-exploding gradients, which ensure a well-posed training process. Finally, we demonstrate the robustness of CH-NODEs on the MNIST image classification problem with noisy test data.
