British Colloquium for Theoretical Computer Science (BCTCS) 2021
Machine Learning (ML) has had a remarkable impact on society. Everything from the phones in our pockets, to the cars that we drive, are being increasingly outfitted with this progressively sophisticated suite of algorithms. But while many of the most basic and fundamental algorithms from ML can be formally verified and tested for safety without much trouble, the same may not be said for Deep Learning (DL) – a prominent forerunner in the state-of-the-art for ML research. These DL models, while performing simple matrix-to-matrix operations at a micro-level, have evolved in scale far past what is tractable for current formal verification methods – all in the pursuit of improving accuracy and performance. This issue of tractability is unsettling considering that the existence of adversarial examples is well known in the ML community. These adversarial examples occur when very small changes to the input space result in a large change in the output space and cause a miss-classification made by the DL model. In the context of self-driving vehicles, small defects and visual artifacts in the sensor input of the DL model, could lead the vehicle to wrongly conclude a stop sign indicates to continue driving where it should have stopped. While the manufacturers will need to put safe-guards in place to prevent this from happening, we should formally prove the (non)-existence of these adversarial examples in the DL model itself. In this presentation, I present the foundational knowledge for understanding adversarial examples, how we can use the input space to dictate the search space for the existence of these examples, and demonstrate their presence with the use of SAT-solving. This work, as a free and open-source project, provides a framework for ML practitioners to verify their own architectures.