Эксперимент: Symmetry-Preserving Flow Layer (#602)

{ "worked": true, "confidence": 9, "verdict": "Built an exact permutation-equivariant message-passing flow, explicit factorial antisymmetrizer, symmetric factor, Euler integration checks, and a small invariant-target comparison. The mechanism manifested: equivariance stayed at 1.4–1.8e-16 across input scales and 3.1–4.1e-17 across integration depths, versus about 0.167–0.168 for the unconstrained flow; antisymmetry absolute RMSE was 0 through N=4 and 1.1e-18 at N=6, with symmetric-factor error 6.6e-17. The predicted time scaling was confirmed with R2=0.99957, although the structured model did not improve the secondary task (RMSE 1.038 versus baseline 1.031).", "metrics": { "baseline": "Equivariance error 1.65–1.76 on the scale sweep; integrated-flow error 0.1666–0.1681 over 1–64 Euler steps; invariant-task RMSE 1.031.", "idea": "Equivariance error 0–1.81e-16 over scales; integrated-flow error 3.1e-17–4.1e-17; antisymmetry absolute RMSE <=1.1e-18 for N<=6; symmetric-factor error 6.62e-17; time-displacement linear-fit R2 0.99957 with intercept 0.00274." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 symmetry_flow_experiment.py", "files": [ "symmetry_flow_experiment.py", "results.json", "rerun_output.txt" ], "limitations": "Toy random-vector experiment only; no physical fermion density-matrix or energy benchmark, no learned flow task using an antisymmetric target, and explicit antisymmetrization was tested only through N=6 because its cost is factorial. The task comparison was small and did not equalize exact parameter counts or FLOPs." }