Efficient Neural Field Learning via Adaptive Coverage and Focused Sampling

2026-10-01

AI Summary

This study addresses the inefficiency of uniform sampling, which overlooks spatial heterogeneity during implicit neural representation training, and the redundancy inherent in existing adaptive sampling methods. To this end, we propose the ACES framework, which introduces a novel structured sampling mechanism. By decoupling coverage from importance to construct adaptive spatial partitions, ACES ensures comprehensive domain coverage while eliminating redundancy, further prioritizing high-information regions through region-level weighting. We theoretically demonstrate that this partitioning strategy effectively reduces gradient variance with controllable bias. Evaluated on scientific field learning tasks, ACES achieves faster convergence and lower reconstruction errors, significantly outperforming both uniform sampling and point-level adaptive baselines.

Abstract

Implicit neural representations (INRs) provide a flexible framework for modeling high-dimensional continuous fields, but their training is often inefficient due to uniform subsampling that ignores spatial heterogeneity. Existing adaptive sampling methods partially address this issue by prioritizing high-error samples, but typically operate at the point level, often leading to redundant sampling in localized regions and insufficient coverage of the domain. We propose ACES (Adaptive Coverage-aware Efficient Sampling), a structured sampling framework that improves training efficiency by decoupling coverage and importance. ACES constructs adaptive spatial partitions to ensure domain coverage and reduce redundancy, and applies region-level importance weighting to prioritize informative regions during training. We provide a theoretical analysis showing that adaptive partitioning reduces gradient variance by increasing within-region homogeneity, and that controlled bias in region-level weighting may improve optimization efficiency relative to standard unbiased estimators. Experiments on scientific field learning tasks demonstrate that ACES achieves faster convergence and lower error than uniform and pointwise adaptive sampling baselines, with the largest gains in fields with highly localized complexity.

Problem

• Implicit Neural Representations
• Adaptive Sampling
• Training Efficiency
• Spatial Heterogeneity
• Domain Coverage

Innovation

• Implicit Neural Representations
• Adaptive Sampling
• Spatial Partitioning
• Importance Weighting
• Gradient Variance Reduction