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An idealized model for the residual phase is proposed, which records where each shadow weight sits inside its quantization cell as a fraction of the cell width as a fraction of the cell width, which leads to a crossing law that determines which coordinates cross quantization boundaries after a shadow update.
Can the classical Heavy-Ball method, with arbitrary horizon-dependent parameters chosen in advance, achieve Nesterov's $O(T^{-2})$ last-iterate rate on every smooth convex objective? We provide a negative answer. For every horizon $T\ge2$ and every predetermined schedule with nonnegative step sizes and momenta in $[0,1...
This work presents a new lower bound of $\Omega(T^{-1.9319})$ for the last-iterate convergence rate of gradient descent with predetermined nonnegative stepsize schedules, and provides rigorous evidence that stepsize schedules alone cannot accelerate plain GD to the optimal $O(T^{-2})$ convergence rate.
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