Эксперимент: Binary-form symmetric-power equivariant layer (#1364)

{ "worked": true, "confidence": 9, "verdict": "Built an exact degree-4 binary symmetric-power representation and a copy-mixing equivariant layer. Polynomial substitution and representation composition matched to about 1e-13, and the constrained layer had zero measured equivariance error versus order-one error for an unconstrained same-size layer. In the tiny classification test both the baseline MLP and invariant feature reached 1.00 accuracy, so the exact equivariance claim was validated but no accuracy win was observed.", "metrics": { "baseline": "MLP test accuracy 1.000; median equivariance-control error 1.284", "idea": "Symmetric-power layer median equivariance error 0.000; max polynomial relative error 3.75e-14; max composition error 7.47e-13; invariant classifier accuracy 1.000" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 symmetric_power_experiment.py", "files": [ "symmetric_power_experiment.py", "results.json" ], "limitations": "The learning comparison is a very small synthetic radius classification task, and the baseline already solves it perfectly. It does not test CNNs, point clouds, shears in a trained task, sample efficiency, FLOPs, or performance on a realistic dataset; the classifier uses a hand-derived invariant rather than a trained deep equivariant network." }