  Formal verification of neural networks is essential for their deployment in
safety-critical areas. Many available formal verification methods have been
shown to be instances of a unified Branch and Bound (BaB) formulation. We
propose a novel framework for designing an effective branching strategy for
BaB. Specifically, we learn a graph neural network (GNN) to imitate the strong
branching heuristic behaviour. Our framework differs from previous methods for
learning to branch in two main aspects. Firstly, our framework directly treats
the neural network we want to verify as a graph input for the GNN. Secondly, we
develop an intuitive forward and backward embedding update schedule.
Empirically, our framework achieves roughly $50\%$ reduction in both the number
of branches and the time required for verification on various convolutional
networks when compared to the best available hand-designed branching strategy.
In addition, we show that our GNN model enjoys both horizontal and vertical
transferability. Horizontally, the model trained on easy properties performs
well on properties of increased difficulty levels. Vertically, the model
trained on small neural networks achieves similar performance on large neural
networks.
