Verification of a trained neural network accuracy

In safety-critical applications it is necessary to verify if a neural net does not display any undesirable behavior due to overtraining. In particular in civil aviation, novel algorithms undergo the utmost scrutiny before the flight software is approved for use in aircraft. Neural nets´ reputation for unpredictability has impeded their use in safety-critical applications. The paper presents a deterministic method for verification of a neural net trained to approximate another, difficult to implement mapping. First, approximation error is evaluated on a uniform grid of testing points. Then, maximal growth rates of both functions are used to bound the error anywhere between the testing points. The technique allows us to verify accuracy of nets that replace large multidimensional look-up tables. Practical ramifications of the method and further possible extensions are discussed