Symbolic Encoding of Neural Networks using Communicating Automata with Applications to Verification of Neural Network Based Controllers

This paper illustrates a way for applying formal methods techniques to specifying and verifying neural networks, with applications in the area of neural network based controllers. Formal methods have some of the characteristics of symbolic models. We describe a communicating automata [Bowman and Gomez, 2005] model of neural networks, where the standard Backpropagation (BP) algorithm [Rumelhart et al., 1986] is applied. Then we undertake a verification of this model using the model checker Uppaal [Behrmann et al., 2004], in order to predict the performance of the learning process. We discuss broad issues of integrating symbolic techniques with complex neural systems. We also argue that symbolic verifications may give theoretically well-founded ways to evaluate and justify neural learning systems.