Green-Margin Residual Dynamics MVP

run_experiment.py implements a finite-horizon Green-kernel calculation for a diagonal contracting/expanding backbone, scalar fixed-point verification, and a small matched 20-layer residual linear-regression comparison. results.json contains the raw output.

Toy mechanism verification

Backbone: scalar stable multiplier a=0.7, so the infinite-horizon Green norm is Gamma=1/(1-a)=3.3333, and perturbation gain is Lambda=eta.

| Prediction | Predicted | Observed | Result | |---|---:|---:|---| | q slope versus eta = LambdaGamma | 3.3333 | 3.3333 | exact | | contraction boundary eta_c=1/(LambdaGamma) | 0.3000 | 0.3159 | 5.3% error | | response gain = 1/(1-q) | 1.2, 1.5, 2, 3, 5, 10, 30 | same values; max relative error 1.8e-15 | exact |

The boundary uses a finite 300-step convergence/divergence test, so its observed threshold is slightly above the asymptotic value. A mixed diagonal backbone also produced finite Green norms for both stable (a=.7) and unstable (a=1.15, backward Green branch) channels: 3.333 and 6.399.

Mini experiment

CUDA was used. Both models have the same depth, width, and parameterization. The margin model rescales residual maps whenever its estimated Green margin exceeds target q0=.8.

| Metric | Baseline | Green-margin | |---|---:|---:| | final MSE | 0.17585 | 0.26123 | | max parameter gradient | 8.0576 | 0.3305 | | final raw q estimate | 5.1004 | 76.8434 | | final effective q after scale | 5.1004 | 0.8000 | | final residual scale | 1.0 | 0.01041 |

Thus the certificate mechanism manifested strongly: the controller maintained effective q at 0.8 and reduced peak gradients by about 24x. It did not improve this tiny regression's loss; the aggressive global rescaling also caused underfitting.

Reproduction

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