Averaged SA-Adam iterates have exactly the SGD Polyak-Ruppert covariance H^{-1} S H^{-1} under sub-linear momentum gain and local stabilization.
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A Polyak-Ruppert Central Limit Theorem for SA-Adam with Momentum and Non-Convergent Adaptive Preconditioning
Averaged SA-Adam iterates have exactly the SGD Polyak-Ruppert covariance H^{-1} S H^{-1} under sub-linear momentum gain and local stabilization.