We present techniques for automatically inferring formal properties of feed-forward neural networks. We observe that a significant part (if not all) of the logic of feed forward networks is captured in the activation status (on or off ) of its neurons. We propose to extract patterns based on neuron decisions as preconditions that imply certain desirable output property e.g., the prediction being a certain class. We present techniques to extract input properties, encoding convex predicates on the input space that imply given output properties and layer properties, representing network properties captured in the hidden layers that imply the desired output behavior. We apply our techniques on networks for the MNIST and ACASXU applications. Our experiments highlight the use of the inferred properties in a variety of tasks, such as explaining predictions, providing robustness guarantees, simplifying proofs, and network distillation.

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Software model checkers, such as JPF, are routinely used to explore executions of programs that have very large state spaces. Sometimes the exploration can take a significant amount of time before a bug is found or the checking is complete, in which case the user must patiently wait, possibly for quite some time, to learn the result of checking. A progress bar that accurately shows the status of the search provides the user useful feedback about the time expected for the search to complete. This paper introduces JPFBar, a novel technique to estimate the percentage of work done by the JPF search by computing weights for the execution paths it explores and summing up the weights. JPFBar is embodied into a listener that prints a progress bar during JPF execution. An experimental evaluation using a variety of Java subjects shows that JPFBar provides accurate information about the search's progress and fares well in comparison with a statebased progress estimator that is part of the standard JPF distribution.