Forward Invariant Polytopes

Forward invariant polytopes are geometric shapes used to analyze and control the behavior of dynamical systems, particularly those involving neural networks. Current research focuses on developing efficient algorithms for constructing and manipulating these polytopes, including methods leveraging Markov Chain Monte Carlo sampling and interval analysis, to certify robustness and analyze network properties like reachability and stability. This work has implications for improving the safety and reliability of AI systems, particularly in safety-critical applications, by providing rigorous guarantees on system behavior within defined operational bounds.