Momentum SGD exhibits two distinct EoSS regimes for batch sharpness, stabilizing at 2(1-β)/η for small batches and 2(1+β)/η for large batches, aligning with linear stability thresholds.
High dimensional analysis reveals conservative sharpening and a stochastic edge of stability.CoRR, abs/2404.19261
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Large loss spikes in SGD are polynomially likely and serve as the dominant mechanism for escaping sharp minima toward flatter solutions in the NTK regime.
Spectral-chaos method paired with Halley's method for fast convergence on stochastic eigenproblems.
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Momentum Further Constrains Sharpness at the Edge of Stochastic Stability
Momentum SGD exhibits two distinct EoSS regimes for batch sharpness, stabilizing at 2(1-β)/η for small batches and 2(1+β)/η for large batches, aligning with linear stability thresholds.
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Large Spikes in Stochastic Gradient Descent: A Large-Deviations View
Large loss spikes in SGD are polynomially likely and serve as the dominant mechanism for escaping sharp minima toward flatter solutions in the NTK regime.
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A Fast-Convergence Resolution of the Stochastic Eigenproblem Using Halley's Method and the Spectral-Chaos Approach
Spectral-chaos method paired with Halley's method for fast convergence on stochastic eigenproblems.