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arXiv Machine Learning By Vihaan Paka-Hegde

How Far is Adam from Natural Gradient Descent?

Read the original on arXiv Machine Learning →

The paper investigates how Adam’s update rule relates to natural gradient descent (NGD) by treating Adam as a diagonal empirical Fisher approximation with additional factors such as diagonal truncation, empirical label substitution, and temporal lag. Using a scale‑invariant metric, the authors quantify Adam’s geometric deviation from true NGD across four loss landscapes—well‑conditioned and ill‑conditioned linear regression, logistic regression, and a small neural network—finding that deviation is low in well‑conditioned settings but can reach about 10³ in ill‑conditioned or non‑convex scenarios. Despite higher geometric drift correlating with slower early optimization, Adam still achieves low final loss, and the improved empirical Fisher (iEF) yields more stable trajectories than the standard empirical Fisher (EF).

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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