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Natural Gradient Descent

introduced 1998 68 papers tagged archive 2025-07-28

archive 2025-07-28 Description, source and code snippet are the archive's method entry.

Natural Gradient Descent is an approximate second-order optimisation method. It has an interpretation as optimizing over a Riemannian manifold using an intrinsic distance metric, which implies the updates are invariant to transformations such as whitening. By using the positive semi-definite (PSD) Gauss-Newton matrix to approximate the (possibly negative definite) Hessian, NGD can often work better than exact second-order methods.

Given the gradient of z, g = (δf(z))/δz, NGD computes the update as:

Δz = αF⁻¹g

where the Fisher information matrix F is defined as:

F = 𝔼_(p(t|z))[∇lnp(t|z)∇lnp(t|z)ᵀ]

The log-likelihood function lnp(t|z) typically corresponds to commonly used error functions such as the cross entropy loss.

Source: LOGAN

Image: Fast Convergence of Natural Gradient Descent for Overparameterized Neural Networks

Papers archive 2025-07-28

30 shown of 68, newest first. Repository counts are the archive's code-links table. A Syntology line states what Syntology ran from that paper's harvested code; it is per sample and not a correctness claim.

Tasks archive 2025-07-28

20 shown of 51 tasks the archive attaches to papers tagged with this method, by distinct papers. A task without a page in the catalog is plain text.

TaskPapers
Variational Inference8
Image Classification7
image-classification7
Second-order methods5
Computational Efficiency4
Deep Learning3
Quantum Machine Learning3
Stochastic Optimization3
Variational Monte Carlo3
BIG-bench Machine Learning2
Bayesian Inference2
Bias Detection2
Clustering2
Federated Learning2
Image Reconstruction2
Language Modeling2
Language Modelling2
regression2
3D Reconstruction1
Adversarial Attack1

Usage over time archive 2025-07-28

Papers per year tagged with Natural Gradient Descent: 2019 to 2025, peak 20 20 0 2019: 5 papers 2019 2020: 9 papers 2020 2021: 12 papers 2021 2022: 9 papers 2022 2023: 8 papers 2023 2024: 20 papers 2024 2025: 5 papers 2025
Papers per year the archive tags with this method, by the paper's archive date (68 dated). Bars are counts, not a trend claim.

Components: the archive holds no method-to-method composition, so PwC's Components table cannot be rebuilt; the Papers list carries no Results column for the same reason (the archive does not join its leaderboard rows to method tags).

Categories archive 2025-07-28

Optimization

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