Natural Gradient Methods

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Overview

Natural gradient methods study how to use the geometry of a model’s probability distributions, commonly represented by the Fisher information matrix, to choose updates that are less dependent on parameterization. They matter when ordinary gradients are poorly scaled or constrained, including neural-network training, policy optimization in reinforcement learning, variational inference, and optimization on manifolds. Approaches range from exact Fisher-based updates to Kronecker-factored, low-rank, and matrix-free approximations, alongside Riemannian methods and convergence analyses for policy learning and other structured problems. A central tension is that curvature-aware updates can improve convergence, but estimating and applying them can be costly or noisy, and useful step sizes and reliable scaling remain challenging.

Latest papers

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29 papers4 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

  1. Ascent Conditions for Length-Normalized Single-Rollout Policy Updates

    Oct 10, 2026Levin David SchwabU-StatisticsPolicy Gradient Methods

  2. What a Reporting Convention Hides: A Matched-Budget Audit of Quantum Natural Gradient with an Exactly Computed Metric

    Oct 7, 2026Lu Wei, Yufeng Wang, Haibin LingQuantum Machine LearningVariational Quantum Algorithms

    Stony Brook University · Westlake University

  3. How Inefficient Is Natural Gradient Descent? From Exact Optimality to Θ( \sqrt{ \log d } ) Divergence

    Oct 5, 2026Guni Sharon, Alan KuhnleInformation GeometryRiemannian Optimization

    Department of Computer Science and Engineering, Texas A&M University, College Station, TX 77843, USA.

  4. Optimizer Geometry Sets the Pace: Spectral Learning Dynamics in Matrix Factorization

    Oct 3, 2026Mahalakshmi Sabanayagam, Simon LuceyGradient Descent DynamicsSpectral Bias

    Australian Institute for Machine Learning, Adelaide University

  5. The cost of useful natural gradient updates

    Sep 27, 2026Subhransu S. Bhattacharjee, Dylan Campbell, Rahul ShomeSample ComplexityNatural Gradient Methods

    School of Computing, The Australian National University

  6. Newton Matching for Generative Modeling: A Unified Framework for Fine-Tuning and Sampling

    Sep 4, 2026Zeyang Li, Yunan Wang, Paolo Giaretta +1Generative ModelingRL for Generative Models

    Massachusetts Institute of Technology

  7. Integer Natural Evolution Strategies

    Aug 24, 2026Jacob de Nobel, Diederick Vermetten, Hao Wang +3Evolution StrategiesNatural Gradient Methods

    Leiden University, Leiden, The Netherlands · Sorbonne Université, CNRS, LIP6, Paris, France · Tel-Hai - University of Kiryat Shmona in the Galilee, Israel +1

  8. Unregularized Convergence of Single-Loop, Entropy-Regularized Natural Actor-Critic

    Aug 20, 2026Zhiqiang TanPolicy OptimizationActor-Critic Methods

    Department of Statistics, Rutgers University. Address: 110 Frelinghuysen Road, Piscataway, NJ 08854.

  9. Efficient Hypergradient Descent for Inverse Reinforcement Learning

    Aug 11, 2026Nikita Sevriukov, Anna Barabanova, Uliana Gagarina +4Reinforcement LearningGradient Descent

    HSE University Moscow, Russia

  10. Fisher8: Stabilizing Neural Heteroscedastic Regression via Output-Layer Fisher Geometry

    Aug 11, 2026Sumedh Vemuganti, Nickvash KaniNatural Gradient MethodsHeteroscedastic Regression

    Electrical and Computer Engineering Department, University of Illinois at Urbana-Champaign

  11. Information-Geometric Forward Policy Training in GFlowNets

    Aug 4, 2026Yordan Raykov, Rodrigo VeigaInformation GeometryNatural Gradient Methods

    School of Mathematical Sciences, University of Nottingham, Nottingham, UK

  12. Finite-Time Analysis of the Natural Policy Gradient in Finite-Horizon Markov Decision Processes

    Jul 25, 2026Asha Barua, Sajad KhodadadianPolicy GradientMarkov Decision Processes

    Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA.

  13. Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers

    Jul 24, 2026Zhangyong Liang, Huanhuan GaoNeural PDE SolversRiemannian Optimization

    National Center for Applied Mathematics Tianjin University Tianjin, 300072, China · School of Mechanical and Aerospace Engineering Jilin University Changchun, 130025, China

  14. Differentially Private Natural Gradient Descent

    Jul 7, 2026Pan Li, Kai Chen, Shuai Chang +3Gradient DescentNatural Gradient Methods

    Institute of Information Engineering, Chinese Academy of Sciences Beijing, China · Department of Computer Science, Metropolitan College, Boston University Boston, United States · Nanyang Technological University Singapore, Singapore

  15. On the Optimizer Dependence of Neural Scaling Laws

    May 28, 2026Vansh Ramani, Shourya Vir JainNatural Gradient MethodsNeural Network Optimization

    Department of Computer Science and Engineering, Indian Institute of Technology Delhi · Department of Electrical Engineering, Indian Institute of Technology Delhi

  16. Randomized Advantage Transformation (RAT): Computing Natural Policy Gradients via Direct Backpropagation

    May 18, 2026Mingfei SunPolicy GradientNatural Gradient Methods

    The University of Manchester, United Kingdom.

  17. Adaptive Stochastic Natural Gradient Method for Safe Optimization on Binary Space

    May 18, 2026Kento Uchida, Ryoki Hamano, Masahiro Nomura +1Black-Box OptimizationNatural Gradient Methods

    Yokohama National University Yokohama, Kanagawa, Japan · CyberAgent Shibuya, Tokyo, Japan · Institute of Science Tokyo Meguro, Tokyo, Japan

  18. Natural Policy Gradient as Doubly Smoothed Policy Iteration: A Bellman-Operator Framework

    May 11, 2026Phalguni Nanda, Zaiwei ChenPolicy GradientReinforcement Learning

    Edwardson School of Industrial Engineering, Purdue University

  19. Natural gradient descent with momentum

    Apr 16, 2026Anthony Nouy, Agustín SomacalDeep Learning OptimizationRiemannian Optimization

    Centrale Nantes, Nantes Universit´e, Laboratoire de Math´ematiques Jean Leray UMR CNRS 6629

  20. Natural Gradient Gaussian Approximation Filter on Lie Groups for Robot State Estimation

    Apr 11, 2026Tianyi Zhang, Wenhan Cao, Chang Liu +2Robot State EstimationBayesian Filtering

    School of Vehicle and Mobility, Tsinghua University, Beijing, China · College of Engineering, Peking University, Beijing, China · School of Vehicle and Mobility and College of Artificial Intelligence, Tsinghua University, Beijing, China

  21. Natural Riemannian gradient for learning functional tensor networks

    Apr 10, 2026Nikolas Klug, Michael Ulbrich, André Uschmajew +1Tensor NetworksRiemannian Optimization

    Institute of Mathematics, University of Augsburg, 86159 Augsburg, Germany · Department of Mathematics, Technical University of Munich, 85748 Garching b. München, Germany · Institute of Mathematics & Centre for Advanced Analytics and Predictive Sciences, University of Augsburg, 86159 Augsburg, Germany

  22. Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks

    Apr 6, 2026Anas Jnini, Elham Kiyani, Khemraj Shukla +5Physics-Informed MLNeural PDE Solvers

    Department of Information Engineering and Computer Science, University of Trento, Trento, Italy · Division of Applied Mathematics, Brown University, Providence, RI, USA · Departament de Física, Universitat d’Alacant, Spain +3

  23. Inversion-Free Natural Gradient Descent on Riemannian Manifolds

    Apr 3, 2026Dario Draca, Takuo Matsubara, Minh-Ngoc TranNatural Gradient MethodsRiemannian Optimization

    School of Mathematics and Statistics, University of Sydney, Australia · University of Sydney Business School, Australia

  24. Sven: Singular Value Descent as a Computationally Efficient Natural Gradient Method

    Apr 1, 2026Samuel Bright-Thonney, Thomas R. Harvey, Andre Lukas +1Deep Learning OptimizationNatural Gradient Methods

    Department of Physics, Massachusetts Institute of Technology · The NSF Institute for Artificial Intelligence and Fundamental Interactions · Rudolf Peierls Centre for Theoretical Physics, University of Oxford +2

  25. Inverse-Free Sparse Variational Gaussian Processes

    Apr 1, 2026Stefano Cortinovis, Laurence Aitchison, Stefanos Eleftheriadis +1Sparse Gaussian ProcessesGaussian Processes

    University of Oxford · University of Bristol

  26. Natural Gradient Descent for Online Continual Learning

    Mar 21, 2026Joe Khawand, David ColliauxKronecker-Factored ApproximationOnline Continual Learning

    Ecole Polytechnique & Télécom Paris Paris, France · Sony Computer Science Laboratories Paris, France

  27. Riemannian Optimization in Modular Systems

    Mar 4, 2026Christian Pehle, Jean-Jacques SlotineContraction TheoryRiemannian Optimization

    Cold Spring Harbor Laboratory Cold Spring Harbor, NY 11724 · Massachusetts Institute of Technology Cambridge, MA 02139

  28. TENG-BC: Unified Time-Evolving Natural Gradient for Neural PDE Solvers with General Boundary Conditions

    Feb 28, 2026Hongjie Jiang, Di LuoNeural PDE SolversPDE Solving

    School of Mathematical Sciences, Peking University, Beijing, China · Department of Physics, Tsinghua University, Beijing, China · Institute of Advanced Study, Tsinghua University, Beijing, China

  29. Fisher-Rao Gradient Flows of Linear Programs and State-Action Natural Policy Gradients

    Mar 28, 2024Johannes Müller, Semih Çaycı, Guido MontúfarPolicy GradientOptimization Convergence Analysis

    Department of Mathematics, RWTH Aachen University, Aachen, 52062, Germany · Departments of Mathematics and Statistics & Data Science, University of California, Los Angeles, 90095, USA · Max Planck Institute for Mathematics in the Sciences, Leipzig, 04103, Germany