Эксперимент: Polar Slack Attention (#1228)

{ "worked": false, "confidence": 9, "verdict": "Built a readable polar-slack module and deterministic verification experiment. For the tetrahedral spherical 2-design with U=-I, h=1, and c=1/3, A is effectively (4/3)I, has three incidence zeros per row, rank 4=d+1, and the Gram term has rank 3 with singular values 4/3. The geometric log-bias gives perfect target selection in the toy proxy, but ordinary top-1 already retains one edge per row, so no improvement over that baseline was observed; arbitrary supports also produced negative slack entries.", "metrics": { "baseline": "Dense attention: target probability 0.24655, cross-entropy 1.72943, 4 edges/row; ordinary top-1 accuracy 0.24338, 1 edge/row.", "idea": "Polar slack: target probability 0.99999994, cross-entropy 6.02e-08, argmax accuracy 1.0, 1 effective positive edge/row after tolerance; exact slack min -1.11e-16 from roundoff, rank 4." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "polar_slack.py", "run_experiment.py" ], "limitations": "No trained Transformer, CIFAR-10, language-model, GPU speed, memory, FLOP, or seed-to-seed training comparison was run. The exact tetrahedral case is highly structured and makes the geometric mask essentially an identity mask; it does not test larger spherical designs or learned h/U. The invalid-support test shows that the paper's nonnegativity guarantee cannot be assumed for unconstrained ML relaxations." }