Эксперимент: Poisson-Kernel Random Attractor Regularizer (#405)

{ "worked": true, "confidence": 9, "verdict": "Built a Poisson-kernel regularizer module, exact toy verification, and a matched small recurrent forecasting experiment. The mechanism manifested: Poisson normalization error was below 2.3e-14, finite-composition attractor error followed the predicted q^K law with relative slope errors below 6e-10, and empirical phase KL to P_x remained about 1e-4 while KL to uniform increased from 0.00012 to 1.015 as |x| grew. In the RNN, the regularizer reduced latent pairwise distance from 0.7544 to 0.7215 and PK NLL from 0.1882 to -0.0391, but validation MSE slightly worsened from 0.02756 to 0.02763, so this supports the mechanism rather than demonstrating a task-performance win.", "metrics": { "baseline": "RNN validation MSE 0.027555; latent pairwise distance 0.754402; PK NLL 0.188178", "idea": "RNN validation MSE 0.027630; latent pairwise distance 0.721493; PK NLL -0.039106; toy normalization max error 2.20e-14; contraction relative slope errors for q=(0.2,0.5,0.8): (5.3e-10,1.3e-14,5.0e-16)" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py && /home/maxwelhelp/main/bin/python3 mini_rnn.py", "files": [ "pk_regularizer.py", "run_experiment.py", "mini_rnn.py", "toy_results.json", "mini_results.json" ], "limitations": "The toy contraction uses affine disk maps rather than full random Blaschke products, and the neural test used one fixed attractor, one regularization coefficient, one K-like depth, and one seed. No sequential-MNIST benchmark, K sweep in the RNN, long-rollout calibration, or statistically repeated runs were tested." }