Reachability analysis of neural networks using mixed monotonicity
This work addresses the need for scalable and general reachability analysis in neural network verification, though it is incremental as it adapts an existing method from dynamical systems.
The paper tackles the problem of computing tight interval over-approximations for neural network outputs under input uncertainty, achieving generality by handling any Lipschitz-continuous activation function and comparing favorably to five existing tools on benchmarks and random networks.
This paper presents a new reachability analysis approach to compute interval over-approximations of the output set of feedforward neural networks with input uncertainty. We adapt to neural networks an existing mixed-monotonicity method for the reachability analysis of dynamical systems and apply it to each partial network within the main network. This ensures that the intersection of the obtained results is the tightest interval over-approximation of the output of each layer that can be obtained using mixed-monotonicity on any partial network decomposition. Unlike other tools in the literature focusing on small classes of piecewise-affine or monotone activation functions, the main strength of our approach is its generality: it can handle neural networks with any Lipschitz-continuous activation function. In addition, the simplicity of our framework allows users to very easily add unimplemented activation functions, by simply providing the function, its derivative and the global argmin and argmax of the derivative. Our algorithm is compared to five other interval-based tools (Interval Bound Propagation, ReluVal, Neurify, VeriNet, CROWN) on both existing benchmarks and two sets of small and large randomly generated networks for four activation functions (ReLU, TanH, ELU, SiLU).