Distribution of hitting times for dissipative random dynamical systems on R d, with application to stochastic gradient descent

arXiv:2609.30274 · stat.ML, cs.LG, math.DS · Submitted 2026-08-11 · Read on arXiv

stat.ML, cs.LG, math.DS

Submitted: 2026-08-11

Updated: 2026-08-11

Terminology

• Stochastic Gradient Descent — 15× in this paper
• Regularization — 5× in this paper · explained in 3 episodes
• Generalization — 4× in this paper · explained in 13 episodes
• Transformer — 4× in this paper · explained in 2 episodes
• Adam — 3× in this paper · explained in 2 episodes
• Lyapunov function — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Adaptation — 1× in this paper · explained in 1 episode
• Attention Mechanism — 1× in this paper · explained in 3 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Distribution Shift — 1× in this paper · explained in 6 episodes
• Langevin Dynamics — 1× in this paper · explained in 2 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Scaling Laws — 1× in this paper · explained in 4 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Spectral Gap — 1× in this paper · explained in 5 episodes
• Stochastic Gradient Descent (SGD) — 1× in this paper · explained in 5 episodes
• Transformer Architecture — 1× in this paper · explained in 2 episodes

Sources

• Searching for Gravitational-Wave Counterparts using the Transiting Exoplanet Survey Satellite
• What is the long-run distribution of stochastic gradient descent? A large deviations analysis
• The global convergence time of stochastic gradient descent in non-convex landscapes: Sharp estimates via large deviations
• Statistical properties of dynamics. Introduction to the functional analytic approach
• Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory
• Adam: A Method for Stochastic Optimization
• Training of Deep Neural Networks based on Distance Measures using RMSProp
• On Linear Stability of SGD and Input-Smoothness of Neural Networks
• Deep Learning is Not So Mysterious or Different

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