PSGD-QEQ equals KL-AIRM up to step size, author corrects gradient uniqueness claim

YouJiacheng · x · 2026-09-10

The author corrects an earlier claim: requiring the gradient to depend linearly on Σ makes the Euclidean gradient unique up to a change of basis, so KL and PSGD objectives yield identical updates under the same geometry. A further derivation shows the gradient isn't truly unique but coincidentally offset by geometry differences — since dp=d(q²)=2qdq=-2q²r=-2pr, PSGD-QEQ equals KL-AIRM up to a step size.

Related event: Correction: PSGD and KL-AIRM Gradients Differ Only by a Step Size(2 posts)→

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