# Krylov Resonance Regularization MVP

`experiment.py` implements a small matrix-pencil/Krylov pole estimator from autocorrelations and applies a detached resonance-triggered spectral-norm penalty in a nonlinear linear-memory RNN. It also runs a controlled two-mode correlation sanity check.

Run:

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

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

The controlled check recovered poles near 0.93 and 0.62 from an exact two-mode correlation sequence. In the delayed-copy mini-task, however, the resonance variant had higher MSE and higher learned spectral radius than the baseline. Thus this MVP does not demonstrate the promised training/stability improvement.

Important limitation: the current training penalty uses the fitted pole estimate as a detached trigger multiplying a differentiable operator-norm proxy; it is not a fully differentiable Hankel/pole loss. The free-running correlation probe is also deliberately tiny and noisy, and no delayed-MNIST, S4, LRU, or orthogonal-RNN comparison was attempted.