Randomized approach to verification of neural networks

Rigorous verification of neural nets is necessary in safety-critical applications such as commercial aviation. This paper investigates feasibility of a randomized approach to the problem. The previously developed deterministic verification method suffers from exponential growth of computational complexity as a function of problem dimensionality, which limits its applicability to low dimensional cases. In contrast, complexity of the randomized method is independent from the problem dimension. Verification of a neural net is formulated as Monte Carlo estimation of probability of failure. The required number of random samples is analyzed. Instead of the general Chernov-based bound, a significantly improved condition is found by exploiting the special case when the number of observed failures is zero. It is shown that with the currently available computers the method is a viable alternative to the deterministic technique. Issues regarding possible acceptance of statistical verification by certification authorities are also, briefly discussed.

[1]  R. Caflisch.  Monte Carlo and quasi-Monte Carlo methods , 1998, Acta Numerica.

[2]  R. R. Zakrzewski.  Verification of a trained neural network accuracy , 2001, IJCNN'01. International Joint Conference on Neural Networks. Proceedings (Cat. No.01CH37222).

[3]  Wen Wu,et al.  Towards Developing Verifiable Neural Network Controller , 1996 .

[4]  Johann Schumann,et al.  A tool for verification and validation of neural network based adaptive controllers for high assurance systems , 2004, Eighth IEEE International Symposium on High Assurance Systems Engineering, 2004. Proceedings..

[5]  Ali Mili,et al.  Towards the Verification and Validation of Online Learning Adaptive Systems , 2003 .

[6]  R. R. Zakrzewski.  Verification of performance of a neural network estimator , 2002, Proceedings of the 2002 International Joint Conference on Neural Networks. IJCNN'02 (Cat. No.02CH37290).

[7]  Mathukumalli Vidyasagar,et al.  Statistical learning theory and randomized algorithms for control , 1998 .

[8]  Johann Schumann,et al.  Toward V&V of neural network based controllers , 2002, WOSS '02.