Reachability Analysis for Feed-Forward Neural Networks using Face Lattices
This addresses the safety verification problem for neural networks in critical applications, representing an incremental improvement in efficiency for existing methods.
The paper tackles the lack of formal safety analysis for deep neural networks by proposing a parallelizable technique to compute exact reachable sets for feed-forward networks with ReLU activations, achieving significantly higher efficiency compared to state-of-the-art methods like Reluplex, Marabou, and NNV.
Deep neural networks have been widely applied as an effective approach to handle complex and practical problems. However, one of the most fundamental open problems is the lack of formal methods to analyze the safety of their behaviors. To address this challenge, we propose a parallelizable technique to compute exact reachable sets of a neural network to an input set. Our method currently focuses on feed-forward neural networks with ReLU activation functions. One of the primary challenges for polytope-based approaches is identifying the intersection between intermediate polytopes and hyperplanes from neurons. In this regard, we present a new approach to construct the polytopes with the face lattice, a complete combinatorial structure. The correctness and performance of our methodology are evaluated by verifying the safety of ACAS Xu networks and other benchmarks. Compared to state-of-the-art methods such as Reluplex, Marabou, and NNV, our approach exhibits a significantly higher efficiency. Additionally, our approach is capable of constructing the complete input set given an output set, so that any input that leads to safety violation can be tracked.