Feature-wise Lipschitz Neural Network

Existing Lipschitz-constrained neural networks typically impose a single global bound on input sensitivity. When sensitivity requirements differ across features and apply only to a selected subset, a global bound can unnecessarily constrain the remaining features and limit how accurately the target function can be approximated. We therefore propose Feature-wise Lipschitz Neural Networks (FLNN), an architecture that imposes distinct sensitivity bounds on selected features while leaving the remaining features unconstrained. The architecture uses controlled and uncontrolled branches that interact across layers while preserving the prescribed sensitivity bounds throughout training. We establish feature-wise Lipschitz guarantees and prove universal approximation of continuous functions satisfying the same constraints on compact domains. A coordinate-wise input transformation further extends the sensitivity guarantees to bounds that vary across regions within the domain of each controlled feature. Experiments on synthetic and real-world datasets demonstrate constraint satisfaction and assess predictive performance under the prescribed sensitivity bounds.