  We propose a spurious region guided refinement approach for robustness
verification of deep neural networks. Our method starts with applying the
DeepPoly abstract domain to analyze the network. If the robustness property
cannot be verified, the result is inconclusive. Due to the over-approximation,
the computed region in the abstraction may be spurious in the sense that it
does not contain any true counterexample. Our goal is to identify such spurious
regions and use them to guide the abstraction refinement. The core idea is to
make use of the obtained constraints of the abstraction to infer new bounds for
the neurons. This is achieved by linear programming techniques. With the new
bounds, we iteratively apply DeepPoly, aiming to eliminate spurious regions. We
have implemented our approach in a prototypical tool DeepSRGR. Experimental
results show that a large amount of regions can be identified as spurious, and
as a result, the precision of DeepPoly can be significantly improved. As a side
contribution, we show that our approach can be applied to verify quantitative
robustness properties.
