We present a scalable and precise verifier for recurrent neural networks, called Prover based on two novel ideas: (i) a method to compute a set of polyhedral abstractions for the non-convex and nonlinear recurrent update functions by combining sampling, optimization, and Fermat's theorem, and (ii) a gradient descent based algorithm for abstraction refinement guided by the certification problem that combines multiple abstractions for each neuron. Using Prover, we present the first study of certifying a non-trivial use case of recurrent neural networks, namely speech classification. To achieve this, we additionally develop custom abstractions for the non-linear speech preprocessing pipeline. Our evaluation shows that Prover successfully verifies several challenging recurrent models in computer vision, speech, and motion sensor data classification beyond the reach of prior work.
@article{arxiv.2005.13300,
title = {Scalable Polyhedral Verification of Recurrent Neural Networks},
author = {Wonryong Ryou and Jiayu Chen and Mislav Balunovic and Gagandeep Singh and Andrei Dan and Martin Vechev},
journal= {arXiv preprint arXiv:2005.13300},
year = {2021}
}