Noise-Triggered Latent Rank Adaptation

experiment.py implements a small rank controller using an exponentially weighted covariance estimate, explicit isotropic noise subtraction, ordered eigenvalues, persistence M, and hysteretic on/off thresholds. switched_rank_demo applies the controller to a stream whose latent order is 2, then 5, then 2.

Run

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

Results are written to results.json.

Quantitative checks

1. Spectral boundary: with signal variance ratio q and noise variance 1, corrected population eigenvalue is q; the predicted activation boundary is q > c_on = 2. The deterministic sweep transitions between q=2.0 and q=2.1, exactly confirming the strict threshold. A finite noisy sweep gives a softer 50% transition near 1.7 because the EWMA estimate and random samples fluctuate.
2. EWMA adaptation delay: for alpha=0.1, old total variance 1.2, new total variance 6, and threshold total variance 3, the analytic first crossing is 7 updates. Thirty noisy trials produce median 6 and mean 6.5 updates.
3. Hysteresis: near threshold, hysteresis (c_on=2, c_off=1.2) gives 105 toggles versus 179 for the single-threshold comparison, a 41.3% reduction.

The reconstruction demo obtains mean active ranks 1.98, 4.87, and 2.07 in the three segments. Adaptive MSE is 0.0896, versus 0.3072 for fixed rank 2 and 0.1232 for fixed rank 5 in this deliberately simple observation/reconstruction benchmark.