PSGD Optimizer Objective Found Identical to KL-Shampoo

YouJiacheng discovered that the PSGD optimizer's objective function in a recent paper is identical to KL-shampoo, and that PSGD's original objective combined with the QEQ update rule yields exactly the same updates as KL+AIRM, revealing deep mathematical connections between the methods.

2026-08-31 ~ 2026-08-31 · 3 related posts

• PSGD cost function matches KL-shampoo objective exactly, author notes — YouJiacheng · 2026-08-31
• PSGD's QEQ update rule yields same rule as KL+AIRM — YouJiacheng · 2026-08-31
• Euclidean gradient uniqueness under Σ dependency — YouJiacheng · 2026-08-31