Geometric Neural Process Fields

2025-02-04

AI Summary

This work addresses the poor generalization of neural fields (NeFs) under few-shot settings. We propose a probabilistic neural radiance field framework that introduces a novel hierarchical latent variable model incorporating geometric basis functions, explicitly modeling predictive uncertainty and embedding multi-scale spatial structural priors. By integrating probabilistic neural processes with hierarchical variational inference, our method enables robust Bayesian adaptation of implicit neural representations (INRs). Evaluated on 3D novel-view synthesis, 2D image reconstruction, and 1D signal regression, the approach significantly improves few-shot generalization performance and uncertainty calibration accuracy. Our framework establishes an interpretable, scalable probabilistic modeling paradigm for reliable deployment of neural fields.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

This paper addresses the challenge of Neural Field (NeF) generalization, where models must efficiently adapt to new signals given only a few observations. 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 our method in capturing uncertainty and leveraging structural information for improved generalization.

Problem

• Neural Field generalization challenge
• Probabilistic framework for radiance fields
• Hierarchical latent variable model design

Innovation

• Probabilistic framework for neural radiance fields
• Hierarchical latent variable model integration
• Geometric bases for spatial structure encoding