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[2602.00099] Gauss-Newton Natural Gradient Descent for Shape Learning
Summary
This paper presents the Gauss-Newton method for optimization in shape learning, demonstrating faster convergence and improved accuracy over traditional methods in benchmark tasks.
Why It Matters
The Gauss-Newton method addresses critical challenges in shape learning, such as ill-conditioning and optimization mismatches, making it a significant advancement in machine learning techniques. Its efficiency can enhance applications in computer vision and robotics, where shape representation is crucial.
Key Takeaways
- Gauss-Newton method offers faster and more stable convergence for shape learning.
- Significantly reduces the number of iterations needed compared to first-order methods.
- Improves both training speed and final solution accuracy in shape optimization tasks.
- Addresses ill-conditioning and optimization mismatches effectively.
- Demonstrated through experiments on benchmark shape optimization tasks.
Computer Science > Machine Learning arXiv:2602.00099 (cs) [Submitted on 24 Jan 2026 (v1), last revised 13 Feb 2026 (this version, v2)] Title:Gauss-Newton Natural Gradient Descent for Shape Learning Authors:James King, Arturs Berzins, Siddhartha Mishra, Marius Zeinhofer View a PDF of the paper titled Gauss-Newton Natural Gradient Descent for Shape Learning, by James King and 3 other authors View PDF HTML (experimental) 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. Comments: Subjects: Machine Learning (cs.LG); Optimization and Control (math.OC) Cite as: arXiv:2602.00099 [cs.LG] (or arXiv:2602.00099v2 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2602.00099 Focus to learn more arXiv-issued DOI via DataCite Submission history From: James King [view email] [v1] Sat, 24 Jan 2026 12:41:11 UTC (2...
