ResearchResearch paperEfficiency & Inference · Training & Scaling · Reinforcement Learning1 source · Oct 18, 2026

Sampling and Curvature in First-Exit Comparisons for Momentum SGD

First-exit prediction for momentum SGD depends on sampling information that pointwise gradient laws omit.

Strongly convex finite pools with identical pointwise laws and matched iid momentum dynamics can have different reshuffled exits; even analytic pools with uniformly close pointwise laws can have separated exit probabilities.
For persistent sampling in one dimension, we establish an explicit $O(h)$ mean-exit comparison with a finite-rate switching process under nonvanishing component velocities and step-size conditions; iid sampling instead averages to an ODE.
Retaining realized minibatches and sampled curvature yields finite-window exit brackets beyond this regime.
Exact-real certificates establish finite means at the original tested radii for three ResNet-18 checkpoints and give local finite-mean conditions for tanh and ViT networks; their upper bounds remain loose, and original-radius ViT mean guarantees remain unresolved despite 128 fresh continuation paths.

[1]Sampling and Curvature in First-Exit Comparisons for Momentum SGD
arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 18, 11:24 AM
First-exit prediction for momentum SGD depends on sampling information that pointwise gradient laws omit.
Strongly convex finite pools with identical pointwise laws and matched iid momentum dynamics can have different reshuffled exits; even analytic pools with uniformly close pointwise laws can have separated exit probabilities.

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