Learning Smooth Neural Functions via Lipschitz Regularization

By Hsueh-Ti Derek Liu, Francis Williams, Alec Jacobson, Sanja Fidler, Or Litany. 2022

135 citations recorded by the source corpus.

Neural implicit fields have recently emerged as a useful representation for 3D shapes. These fields are commonly represented as neural networks which map latent descriptors and 3D coordinates to implicit function values. The latent descriptor of a neural field acts as a deformation handle for the 3D shape it represents. Thus, smoothness with respect to this descriptor is paramount for performing shape-editing operations. In this work, we introduce a novel regularization designed to encourage smooth latent spaces in neural fields by penalizing the upper bound on the field’s Lipschitz constant. Compared with prior Lipschitz regularized networks, ours is computationally fast, can be implemented in four lines of code, and requires minimal hyperparameter tuning for geometric applications. We demonstrate the effectiveness of our approach on shape interpolation and extrapolation as well as partial shape reconstruction from 3D point clouds, showing both qualitative and quantitative improvements over existing state-of-the-art and non-regularized baselines.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

On the Effectiveness of Lipschitz-Driven Rehearsal in Continual Learning (2022, methodology): “7 by an additional contribution, one might argue that a similar effect could be obtained by fixing an initial value and force the model to reduce its capacity until it meets the desiderata [48].”