Эксперимент: Gain-Weighted Cluster Co-Design (#424)

{ "worked": true, "confidence": 9, "verdict": "Built a self-contained gain-weighted cluster co-design toy implementation covering diagonal gain normalization, symmetric feedback-score greedy merging, and dominant-cycle visibility. The math checks passed: optimized mu matched the predicted cycle gain with maximum absolute error 1.18e-8, imbalance invariance error was 9.27e-9, and the c=1 stability boundary plus clustering transition were confirmed across sweeps. This is a real mechanism-level effect, but not evidence of improved neural task loss or runtime.", "metrics": { "baseline": "Singleton and fixed random partitions left the dominant cycle boundary gain at c^3: 0.125, 0.729, 1.0, 1.331, and 3.375 for c=0.5, 0.9, 1.0, 1.1, and 1.5.", "idea": "Greedy gain-weighted partition [[0,1,2],[3,4,5]] internalized the dominant cycle for every sweep value, reducing its cross-cluster boundary gain from c^3 to 0.0. Diagonal normalization matched the predicted optimum c with max error 1.18e-8 and removed imbalance dependence with max error 9.27e-9." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "No block-sparse transformer, recurrent model, CIFAR-10 training, JVP gain estimation, learned q during neural optimization, path dynamic programming, communication cost, wall-clock speed, memory, or task-loss comparison was tested. The cluster result is a graph-level certificate/visibility demonstration and does not reduce the full spectral radius of the original graph." }