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Deep neural networks are revolutionizing the way complex systems are designed. Consequently, there is a pressing need for tools and techniques for network analysis and certification. To help in addressing that need, we present Marabou, a framework for verifying deep neural networks. Marabou is an SMT-based tool that can answer queries about a network's properties by transforming these queries into constraint satisfaction problems. It can accommodate networks with different activation functions and topologies, and it performs high-level reasoning on the network that can curtail the search space and improve performance. It also supports parallel execution to further enhance scalability. Marabou accepts multiple input formats, including protocol buffer files generated by the popular TensorFlow framework for neural networks. We describe the system architecture and main components, evaluate the technique and discuss ongoing work.

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One approach to designing decision making logic for an aircraft collision avoidance system frames the problem as a Markov decision process and optimizes the system using dynamic programming. The resulting collision avoidance strategy can be represented as a numeric table. This methodology has been used in the development of the Airborne Collision Avoidance System X (ACAS X) family of collision avoidance systems for manned and unmanned aircraft, but the high dimensionality of the state space leads to very large tables. To improve storage efficiency, a deep neural network is used to approximate the table. With the use of an asymmetric loss function and a gradient descent algorithm, the parameters for this network can be trained to provide accurate estimates of table values while preserving the relative preferences of the possible advisories for each state. By training multiple networks to represent subtables, the network also decreases the required runtime for computing the collision avoidance advisory. Simulation studies show that the network improves the safety and efficiency of the collision avoidance system. Because only the network parameters need to be stored, the required storage space is reduced by a factor of 1000, enabling the collision avoidance system to operate using current avionics systems.