论文标题
关于认证的强大培训和间隔绑定传播的融合
On the Convergence of Certified Robust Training with Interval Bound Propagation
论文作者
论文摘要
到目前为止，当存在潜在的对抗性扰动时，间隔结合传播（IBP）是训练具有可证实鲁棒性的神经网络的最新方法的基础，而在现有文献中，IBP培训的融合仍然未知。在本文中，我们介绍了有关IBP培训收敛性的理论分析。通过过度参数化的假设，我们分析了IBP强大训练的收敛性。我们表明，当使用IBP训练训练具有物流损失的随机初始化的两层恢复神经网络时，如果我们的扰动半径足够小，较大的网络宽度，梯度下降可以线性收敛到零鲁棒训练误差，并具有很高的可能性。
Interval Bound Propagation (IBP) is so far the base of state-of-the-art methods for training neural networks with certifiable robustness guarantees when potential adversarial perturbations present, while the convergence of IBP training remains unknown in existing literature. In this paper, we present a theoretical analysis on the convergence of IBP training. With an overparameterized assumption, we analyze the convergence of IBP robust training. We show that when using IBP training to train a randomly initialized two-layer ReLU neural network with logistic loss, gradient descent can linearly converge to zero robust training error with a high probability if we have sufficiently small perturbation radius and large network width.
