Mathematical and Dynamical Foundations › Key Parameters

The key parameters for the transition-model experiment are:

• n_train: Number of logged steps used to fit both regression models. The rest of the log is held out, so closed-loop rollouts are compared against data the models never saw. Larger values reduce estimation noise in the fitted coefficients but shrink the held-out window available for the stress test, so the split embodies a direct trade-off between fit quality and evaluation power.
• rcond: Cutoff for small singular values passed to np.linalg.lstsq. Design directions whose singular values fall below this fraction of the largest are treated as zero, which keeps the least-squares solve stable when design columns are nearly collinear. In this experiment the design is benign, but in richer feature spaces the same knob controls how aggressively the solver refuses to fit noise directions.
• horizon: Number of closed-loop feedback steps in the stress-test rollout. Longer horizons give compounding error more room to separate a dynamically faithful model from one that is merely accurate one step ahead. Choose it relative to the system's natural timescale: here, a few dozen steps span several full limit cycles, which is enough for amplitude and rhythm errors to become unmistakable.
• temp0: Initial temperature handed to every closed-loop rollout. Matching it to the start of the true evaluation window keeps the gap measurements comparable across models. Because the system's limit cycle erases initial conditions within a handful of steps, this choice matters little for the full model, which is itself a small demonstration of attractor behavior.