  Deep Neural Networks (DNNs) have emerged as a powerful mechanism and are
being increasingly deployed in real-world safety-critical domains. Despite the
widespread success, their complex architecture makes proving any formal
guarantees about them difficult. Identifying how logical notions of high-level
correctness relate to the complex low-level network architecture is a
significant challenge. In this project, we extend the ideas presented in and
introduce a way to bridge the gap between the architecture and the high-level
specifications. Our key insight is that instead of directly proving the safety
properties that are required, we first prove properties that relate closely to
the structure of the neural net and use them to reason about the safety
properties. We build theoretical foundations for our approach, and empirically
evaluate the performance through various experiments, achieving promising
results than the existing approach by identifying a larger region of input
space that guarantees a certain property on the output.

Machine Learning;Neural and Evolutionary Computing;Machine Learning