This work studies the robustness certification problem of neural network
models, which aims to find certified adversary-free regions as large as
possible around data points. In contrast to the existing approaches that seek
regions bounded uniformly along all input features, we consider non-uniform
bounds and use it to study the decision boundary of neural network models. We
formulate our target as an optimization problem with nonlinear constraints.
Then, a framework applicable for general feedforward neural networks is
proposed to bound the output logits so that the relaxed problem can be solved
by the augmented Lagrangian method. Our experiments show the non-uniform bounds
have larger volumes than uniform ones and the geometric similarity of the
non-uniform bounds gives a quantitative, data-agnostic metric of input
features' robustness. Further, compared with normal models, the robust models
have even larger non-uniform bounds and better interpretability.

研究神经网络模型的鲁棒性认证问题，提出一种框架来限制输出标志，以使加宽限制后的问题能够通过增广 Lagrangian 方法来解决，证明了非均匀限制具有更大的体积和更好的鲁棒性，并提供了一种定量的数据 - 不可知度量输入特征的鲁棒性。