langevin-dynamics

Langevin dynamics inject controlled noise into neural network training to analyze exploration, convergence, and discretization effects. This Skill instruments training dynamics by solving Langevin SDEs with multiple discretization solvers, enabling you to observe how temperature, solver choice, and step size alter optimization trajectories and approach equilibrium.

Yes. This Skill computes Fokker-Planck convergence diagnostics to empirically measure proximity to the Gibbs distribution. Run multiple solver configurations across different temperatures and discretization steps to produce comparative trajectories that reveal convergence behavior and mixing time.

This Skill lets you solve the same Langevin SDE with multiple discretization solvers and varying dt parameters, then compare output trajectories side by side. This reveals how different step sizes impact numerical accuracy, exploration efficiency, and convergence rate across solver configurations.

Langevin dynamics use temperature as a noise scaling parameter. This Skill lets you sweep temperature values and observe their effect on training trajectories—higher temperatures increase exploration; lower temperatures favor exploitation. Comparative diagnostics show the trade-off across your chosen loss and gradient terms.

This Skill targets users familiar with SDE theory and neural network training. You define the Langevin SDE by specifying loss, gradient, and temperature terms. Advanced implementation depth means it assumes comfort with convergence analysis, Fokker-Planck equations, and discretization methods like Euler-Maruyama.

Yes. This Skill provides mixing time estimation diagnostics that measure when training equilibrates under Langevin dynamics. By running trajectories across multiple solver configurations and temperature settings, you identify the number of steps needed for stable convergence behavior.