Fine-grained neural network abstraction for efficient formal verification

The advance of deep learning makes it possible to empower safety-critical systems with intelligent capabilities. However, its intelligent component, i.e., deep neural network, is difficult to formally verify due to the large scale and intrinsic complexity of the verification problem. Abstraction has been proved to be an effective way of improving the scalability. A challenging problem in abstraction is that it is difficult to achieve a balance between the size reduced and output overestimation caused by abstraction. In this work, we propose an effective fine-grained approach to abstract neural networks. Our approach is fine-grained in that we identify four cases that should be abstracted independently under a certain neuron prioritization strategy. This allows us to merge more neurons in networks and meanwhile maintain a relatively low output overestimation. Experimental results show that our approach outperforms other existing abstraction approaches by significantly reducing the scale of target deep neural networks with small overestimation.