What question did this study set out to answer?

This research aims to investigate Adam’s geometric relationship with natural gradient descent (NGD) across different loss landscapes.

June 1, 2026Open Access

How Far is Adam from Natural Gradient Descent?

View Full Paper

Ask AI

Bookmark

Authors

VPVihaan Paka-HegdeSan Francisco University High School

Discussion

Member takes

Implication

Randomized trial examines Adam’s geometric deviation from natural gradient descent across various loss landscapes, suggesting unique optimization dynamics.

Key Points

This research aims to investigate Adam’s geometric relationship with natural gradient descent (NGD) across different loss landscapes.
Analyzed Adam's full update rule including momentum as a diagonal empirical Fisher approximation.
Evaluated Adam's performance across well-conditioned and ill-conditioned linear regression, logistic regression, and a small non-convex neural network.
Used the scale-invariant γ(∆θ) metric to measure geometric deviation from true NGD.
Adam’s geometric deviation is low in well-conditioned settings but rises significantly in ill-conditioned landscapes, reaching misalignments of approximately 103 in the neural network.
Higher geometric drift is associated with slower initial optimization but does not impair final loss minimization; Adam consistently achieves low loss.
The improved empirical Fisher (iEF) provides more stable paths compared to the standard empirical Fisher (EF), which is prone to oscillation or divergence.

Cite This Study

Vihaan Paka-Hegde (2026) studied this question.

synapsesocial.com/papers/6a1d22db02fbce9130638882 https://doi.org/10.5281/zenodo.20466393

View Full Paper

Ask AI

Bookmark

Implication

Randomized trial examines Adam’s geometric deviation from natural gradient descent across various loss landscapes, suggesting unique optimization dynamics.

How Far is Adam from Natural Gradient Descent?

Discussion

Member takes

Implication

Key Points

Cite This Study

How Far is Adam from Natural Gradient Descent?

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider