Adam Optimizer's Geometric Relationship to Natural Gradient Descent Examined

VERA Brief

AI-generated. Grounded in the article and its cited sources.

New research examines the geometric relationship between the Adam optimizer and natural gradient descent (NGD). The study found Adam's deviation from NGD is context-dependent, with significant deviations observed under ill-conditioning, though Adam still achieved low loss.

Key facts

• Researchers analyzed Adam's update rule and identified it as a modified diagonal empirical Fisher approximation.
• Adam's geometric deviation from NGD was measured across various loss landscapes, including linear and logistic regression, and a neural network.
• Adam showed low deviation in well-conditioned scenarios but significant deviations under ill-conditioning.
• Higher geometric drift correlated with slower initial optimization but did not negatively impact final objective minimization.
• The study suggests Adam's effectiveness may stem from a balance of approximation errors and momentum smoothing.