# Correctness Verification of Neural Networks

We present the first verification that a neural network produces a correct output within a specified tolerance for every input of interest. We define correctness relative to a specification which identifies 1) a state space consisting of all relevant states of the world and 2) an observation process that produces neural network inputs from the states of the world. Tiling the state and input spaces with a finite number of tiles, obtaining ground truth bounds from the state tiles and network output bounds from the input tiles, then comparing the ground truth and network output bounds delivers an upper bound on the network output error for any input of interest. Results from a case study highlight the ability of our technique to deliver tight error bounds for all inputs of interest and show how the error bounds vary over the state and input spaces.

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