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We present REGLO, a novel methodology for repairing pretrained neural networks to satisfy global robustness and individual fairness properties. A neural network is said to be globally robust with respect to a given input region if and only if all the input points in the region are locally robust. This notion of global robustness also captures the notion of individual fairness as a special case. We prove that any counterexample to a global robustness property must exhibit a corresponding large gradient. For ReLU networks, this result allows us to efficiently identify the linear regions that violate a given global robustness property. By formulating and solving a suitable robust convex optimization problem, REGLO then computes a minimal weight change that will provably repair these violating linear regions. 

This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with artificial intelligence (AI) components. Specifically, machine learning (ML) components in cyber-physical systems (CPS), such as feedforward neural networks used as feedback controllers in closed-loop systems are considered, which is a class of systems classically known as intelligent control systems, or in more modern and specific terms, neural network control systems (NNCS). We more broadly refer to this category as AI and NNCS (AINNCS). The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2020. In the second edition of this AINNCS category at ARCH-COMP, four tools have been applied to solve seven different benchmark problems, (in alphabetical order): NNV, OVERT, ReachNN*, and VenMAS. This report is a snapshot of the current landscape of tools and the types of benchmarks for which these tools are suited. Due to the diversity of problems, lack of a shared hardware platform, and the early stage of the competition, we are not ranking tools in terms of performance, yet the presented results probably provide the most complete assessment of current tools for safety verification of NNCS.