Abstract
We present an approach for the verification of feed-forward neural networks in which all nodes have a piece-wise linear activation function. Such networks are often used in deep learning and have been shown to be hard to verify for modern satisfiability modulo theory (SMT) and integer linear programming (ILP) solvers.
The starting point of our approach is the addition of a global linear approximation of the overall network behavior to the verification problem that helps with SMT-like reasoning over the network behavior. We present a specialized verification algorithm that employs this approximation in a search process in which it infers additional node phases for the non-linear nodes in the network from partial node phase assignments, similar to unit propagation in classical SAT solving. We also show how to infer additional conflict clauses and safe node fixtures from the results of the analysis steps performed during the search. The resulting approach is evaluated on collision avoidance and handwritten digit recognition case studies.
This work was supported by the Institutional Strategy of the University of Bremen, funded by the German Excellence Initiative.
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Notes
- 1.
GNU Linear Programming Kit, http://www.gnu.org/software/glpk/glpk.html.
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Ehlers, R. (2017). Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks. In: D'Souza, D., Narayan Kumar, K. (eds) Automated Technology for Verification and Analysis. ATVA 2017. Lecture Notes in Computer Science(), vol 10482. Springer, Cham. https://doi.org/10.1007/978-3-319-68167-2_19
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