Geometric Neural Process Fields

TMLR Paper5037 Authors

Abstract: Neural Fields (NeFs) offer compact, continuous models of signals and scenes. However, one of the major issues is that a separate neural network has to be trained from scratch for each signal. To tackle this, we propose Geometric Neural Process Fields (G-NPF ), a probabilistic framework for neural radiance fields that explicitly captures uncertainty. We formulate NeF generalization as a probabilistic problem, enabling direct inference of NeF function distributions from limited context observations. To incorporate structural inductive biases, we introduce a set of geometric bases that encode spatial structure and facilitate the inference of NeF function distributions. Building on these bases, we design a hierarchical latent variable model, allowing G-NPF to integrate structural information across multiple spatial levels and effectively parameterize INR functions. This hierarchical approach improves generalization to novel scenes and unseen signals. Experiments on novel-view synthesis for 3D scenes, as well as 2D image and 1D signal regression, demonstrate the effectiveness of G-NPF in capturing uncertainty and leveraging structural information for improved generalization.

Submission Length: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Marcus_A_Brubaker1

Submission Number: 5037