Adaptive reset neural ODE MVP

adaptive_reset_experiment.py implements the paper's discrete stopping rule on a scalar time-varying flow. Each local field is f_theta(y)=theta*y, fit by teacher-forced derivative regression, and the next boundary is the first grid point where the 95th-percentile teacher-vs-model state error exceeds epsilon, subject to minimum and cap lengths. Deployment uses the predicted terminal state as the next reset, while training always fits from teacher states.

Quantitative mechanism checks

For the constant-flow sanity model, teacher dynamics are y'=lambda*y, candidate dynamics are y'=lambda_hat*y, and the exact 95th-percentile error is

E(s) = |exp(lambda*s)-exp(lambda_hat*s)| * quantile_0.95(|y0|).

Thus the predicted boundary is the first root E(s)=epsilon:

1. At fixed mismatch, increasing epsilon increases the boundary. Observed boundaries for epsilon [.005,.01,.02,.04,.08] were [.028,.056,.108,.208,.384]; analytic predictions were [.0279,.0552,.1079,.2070,.3839].
2. At fixed epsilon, larger mismatch causes an earlier boundary. For lambda_hat [.49,.45,.40,.30], observed boundaries were [1.322,.418,.230,.122], versus analytic [1.322,.417,.229,.121].
3. Discrete stopping converges to the analytic first crossing. Across epsilon [.01,.03,.08], maximum absolute grid error was 0.00155, below the dt=.002 resolution tolerance.

Mini experiment

On a time-varying scalar flow over T=12, the shared field had full-rollout RMSE 37.23 and final RMSE 85.42. Adaptive local fields had RMSE 2.50 and final RMSE 5.52, using 166 windows (minimum 4 and cap 35 grid steps). This is a strong drift-reduction signal, but not an equal-parameter or equal-FLOP comparison: the adaptive method gets substantially more local parameters and incurs many resets. The result therefore supports the mechanism, not a claim of compute-normalized superiority.

Run

/home/maxwelhelp/main/bin/python3 adaptive_reset_experiment.py

Outputs are printed and saved to results.json.