Approximate Bisimulation Relations for Neural Networks and Application to Assured Neural Network Compression
This work addresses the need for reliable neural network compression and verification, particularly in safety-critical domains, though it is incremental as it builds on existing reachability analysis methods.
The paper tackles the problem of measuring similarity between neural networks by proposing approximate bisimulation relations, enabling assured compression with quantifiable error bounds, and demonstrates effectiveness by accelerating verification of ACAS Xu neural networks.
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.