In this paper, we propose a concept of approximate bisimulation relation for
feedforward neural networks. In the framework of approximate bisimulation
relation, a novel neural network merging method is developed to compute the
approximate bisimulation error between two neural networks based on
reachability analysis of neural networks. The developed method is able to
quantitatively measure the distance between the outputs of two neural networks
with the same inputs. Then, we apply the approximate bisimulation relation
results to perform neural networks model reduction and compute the compression
precision, i.e., assured neural networks compression. At last, using the
assured neural network compression, we accelerate the verification processes of
ACAS Xu neural networks to illustrate the effectiveness and advantages of our
proposed approximate bisimulation approach.

该论文提出了一种基于近似双模拟关系的神经网络模型缩减方法，利用该方法可以量化两个神经网络的输出距离，从而进行神经网络模型缩减并加速神经网络的验证过程。