Unverified50% confidenceFactExact time
The newly derived stability conditions are complementary to but conceptually distinct from the stability conditions of stochastic gradient descent (SGD).
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10/27/2026
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UnverifiedClassical stochastic approximation theory relies on the Robbins-Monro conditions to guarantee convergence, but SGDM with a constant step size does not satisfy these conditions, and the parameters keep fluctuating around a steady state rather than converging to a point.77% similarUnverifiedSGD stability typically concerns step size and the covariance structure of gradient noise, whereas the new conditions directly relate to the frequency and information content of feedback.77% similarUnverifiedThe paper proves that the SGD iterates converge to a stable OU process at the central fluctuation scale and uses this limit to characterize the tail probabilities.73% similarUnverifiedWhen multiple constraints conflict with one another, the model may randomly favor different constraints, leading to reduced output stability.72% similarUnverifiedWhen ε ≈ 1, the gradient second-moment term in the denominator is diluted, adaptive scaling has almost no effect, and the optimizer behaves close to pure SGD.71% similar
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