Beyond Uniformity: Regularizing Implicit Neural Representations through a Lipschitz Lens

Abstract

Implicit Neural Representations (INRs) have shown great promise in solving inverse problems, but their lack of inherent regularization often leads to a trade-off between expressiveness and smoothness. While Lipschitz continuity presents a principled form of implicit regularization, it is often applied as a rigid, uniform 1-Lipschitz constraint, limiting its potential in inverse problems. In this work, we reframe Lipschitz regularization as a flexible *Lipschitz budget framework*. We propose a method to first derive a principled, task-specific total budget $K$, then proceed to distribute this budget *non-uniformly* across all network components, including linear weights, activations, and embeddings. Across extensive experiments on deformable registration and image inpainting, we show that non-uniform allocation strategies provide a measure to balance regularization and expressiveness within the specified global budget. Our *Lipschitz lens* introduces an alternative, interpretable perspective to Neural Tangent Kernel (NTK) and Fourier analysis frameworks in INRs, offering practitioners actionable principles for improving network architecture and performance.