Gauss-Newton Natural Gradient Descent for Shape Learning

2026-01-24

AI Summary

This work addresses the optimization challenges in shape learning arising from the ill-conditioning of differential constraints and the mismatch between parameter and function spaces. To mitigate these issues, the authors propose incorporating Gauss-Newton natural gradient into the training of implicit neural surfaces and geometry-aware neural networks. This approach effectively alleviates ill-conditioning and bridges the optimization gap between the two spaces. As a result, the method significantly enhances training stability and efficiency, achieving faster convergence, fewer iterations, and higher final accuracy across multiple benchmark tasks compared to existing approaches.

Technology Category

• Machine Learning: Learning with Manifolds
• Natural Language Processing: Learning & Optimization for NLP
• Search and Optimization: Learning to Search

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
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We explore the use of the Gauss-Newton method for optimization in shape learning, including implicit neural surfaces and geometry-informed neural networks. The method addresses key challenges in shape learning, such as the ill-conditioning of the underlying differential constraints and the mismatch between the optimization problem in parameter space and the function space where the problem is naturally posed. This leads to significantly faster and more stable convergence than standard first-order methods, while also requiring far fewer iterations. Experiments across benchmark shape optimization tasks demonstrate that the Gauss-Newton method consistently improves both training speed and final solution accuracy.

Problem

• shape learning
• ill-conditioning
• differential constraints
• function space
• parameter space

Innovation

• Gauss-Newton
• shape learning
• implicit neural surfaces
• natural gradient
• geometry-informed neural networks