Эксперимент: Polyconvex rotation-frame Jacobian loss (#1172)

{ "worked": true, "confidence": 7, "verdict": "Built a reproducible PyTorch MVP with SO(3) rotation frames, autodiff Jacobians, stable cofactor computation, determinant barrier, and lifted polyconvex energy. The rotation/cofactor/determinant identities were verified to about 1.4e-6 absolute error. In the toy deformation experiment both methods had zero folds, while the proposed loss improved mean Jacobian conditioning and minimum determinant at both amplitudes; it slightly improved task MSE at amplitude 1 and was nearly equal at amplitude 2. This is a promising conditioning/stability signal, but not definitive evidence of lower fold rate because the tiny task produced no folds for either method.", "metrics": { "baseline": "amp1: MSE 0.005764, fold fraction 0, mean condition 2.553, min det 0.241; amp2: MSE 0.019627, fold fraction 0, mean condition 4.863, min det 0.0674", "idea": "amp1: MSE 0.004731, fold fraction 0, mean condition 2.380, min det 0.568; amp2: MSE 0.020299, fold fraction 0, mean condition 3.796, min det 0.177" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a small fixed-collocation synthetic warp and one random seed were tested. Rotation smoothness K=R^T Curl R, learned convex energy parameters, larger networks, parameter/FLOP matching, and genuinely folding or noisy registration tasks were not tested; the implementation uses an exponential-map SO(3) head rather than SVD polar projection for numerical stability." }