We study the problem of computing the preimage of a set under a neural network with piecewise-affine activation functions. We recall an old result that the preimage of a polyhedral set is again a union of polyhedral sets and can be effectively computed. We show several applications of computing the preimage for analysis and interpretability of neural networks.

翻译：我们研究了在分段仿射激活函数的神经网络下计算集合原像的问题。我们回顾了一个经典结论：多面体集的原像仍然是多面体集的并集，并且可以高效计算。我们展示了计算原像在神经网络分析与可解释性中的若干应用。