Model based verification of spiking neural networks in cyber physical systems

Spiking Neural Networks (SNNs) have found increasing utility in designing safety-critical Cyber-Physical Systems (CPSs) such as implantable medical devices, autonomous vehicles, and space robotics due to their capability to operate on information represented in temporal coding and exhibit various behavioural modalities. Thus, there has been recent interest in formally verifying their timing behaviours and providing soundness guarantees of their diverse characteristics. However, beyond the simplistic Leaky Integrate and Fire (LIF) model, which only mimics 3 spiking behaviours, there is a lack of unifying methodology in literature to verify complex dynamics of biological neurons exhibiting 20 spiking behaviours as demonstrated by the pioneering work of Izhikevich. There is also a complete lack of formulation for the verification of SNN-based systems. This paper bridges these gaps by proposing a model-based approach for designing SNN-based controllers in CPS. We propose sound structural transformations translating any spiking neuron into networks of Timed Automata (TA), model the complex Izhikevich neural model and formally verify all 20 timing behaviours it exhibits for the first time. We then present two case studies that were modelled as SNNs using our approach: the PID controller, and the Car-Following controller, and subsequently attempt static model checking and statistical verification of their generated TA models for safety guarantees.