Эксперимент: Permutation-Symmetric Quadratic Module (#887)

{ "worked": true, "confidence": 8, "verdict": "Built a permutation-symmetric branch module and its Gram-matrix quadratic approximation in experiment.py. The core mechanism manifested: the remainder scaled as epsilon^3 (observed slope 3.010 vs predicted 3), orthogonal branch mixing changed the original only at cubic order (2.992 vs 3), quadratic output was Gram-invariant (error 4.8e-7), and coherent width scaling was linear (1.000 vs 1). In the tiny fitting test, the full branch baseline substantially outperformed the quadratic approximation, so the mechanism was validated but no task-level accuracy win was observed.", "metrics": { "baseline": "Branch MLP MSE at steps 0/99/249/499: 0.08170, 9.22e-05, 2.14e-05, 1.16e-05", "idea": "Quadratic Gram module MSE at steps 0/99/249/499: 0.08175, 0.01447, 0.01447, 0.01447; parameter count 112 each. Math: epsilon slope 3.010, orthogonal-difference slope 2.992, aligned width slope 1.000, quadratic Gram invariance error 4.8e-7." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a synthetic scalar branch-sum toy was tested, not MNIST/CIFAR, CNNs, attention, low-rank parameterizations, FLOPs, or peak-memory measurements. The random-width exponent was noisy (0.680 rather than exactly 0.5), and the quadratic model was evaluated against a teacher containing a sizable cubic term." }