# 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

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

Outputs are printed and saved to `results.json`.