Bi Lipschitz

Bi-Lipschitz mappings, functions that preserve distances up to a constant factor in both directions, are a focus of current research due to their desirable properties for various applications. Researchers are exploring the use of invertible neural networks, particularly those with architectures designed to guarantee or control bi-Lipschitzness, to approximate and learn these mappings, with a focus on achieving tight control over the Lipschitz constants. This work is significant because bi-Lipschitz properties offer benefits in areas such as approximation theory, handling multisets and point clouds in machine learning, and improving the robustness and interpretability of neural networks.