In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in form of Linear Programming instances, one question is whether there do exist valid inputs such that the network computes a valid output? And does this property hold for all valid inputs? Do two given networks compute the same function? Is there a smaller network computing the same function? The complexity of these questions have been investigated recently from a practical point of view and approximated by heuristic algorithms. We complement these achievements by giving a theoretical framework that enables us to interchange security and efficiency questions in neural networks and analyze their computational complexities. We show that the problems are conquerable in a semi-linear setting, meaning that for piecewise linear activation functions and when the sum- or maximum metric is used, most of them are in P or in NP at most.

我们研究了神经网络计算的形式验证问题，探讨了其各种鲁棒性和最小化问题。我们提供了一个理论框架，使我们能够在神经网络中转换安全性和效率问题，并分析它们的计算复杂性。我们发现，在半线性设置中，对于分段线性激活函数和使用求和或最大度量时，大多数问题都属于P类或最多属于NP类。

神经网络中的鲁棒性验证