2024/06/06 by Sina Sharifi, Sharifi, Sina, Mahyar Fazlyab +1 · 1 citation
Computer Science · #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Neural Networks and Applications #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2406.04476
openalex publication_date 2024/06/06 · openalex created_date 2024/06/11 · openalex updated_date 2026/07/28
We propose a novel reachability analysis method tailored for neural networks with differentiable activations. Our idea hinges on a sound abstraction of the neural network map based on first-order Taylor expansion and bounding the remainder. To this end, we propose a method to compute analytical bounds on the network's first derivative (gradient) and second derivative (Hessian). A key aspect of our method is loop transformation on the activation functions to exploit their monotonicity effectively. The resulting end-to-end abstraction locally preserves the derivative information, yielding accurate bounds on small input sets. Finally, we employ a branch and bound framework for larger input sets to refine the abstraction recursively. We evaluate our method numerically via different examples and compare the results with relevant state-of-the-art methods.