Эксперимент: Fractional Mahalanobis radial head (#1311)

{ "worked": true, "confidence": 6, "verdict": "Built a differentiable fractional Mahalanobis radial head using Cholesky covariance solves, learned centers and covariances, fractional powers, determinant correction, and regularization. Cholesky radii matched explicit Mahalanobis computation to 4.4e-16, while the fractional basis approximated a Student-t radial log-generator with RMSE 0.039 over squared radii 1e-4–100. On the synthetic test, the idea slightly improved test log-loss over the MLP on Gaussian data (0.3014 vs 0.3025) and Student-t data (0.4285 vs 0.4326), but accuracy was essentially unchanged or slightly lower, so this is a modest promising signal rather than a decisive win.", "metrics": { "baseline": "MLP test log-loss/accuracy: Gaussian 0.3025/87.13%; Student-t 0.4326/82.33%. Frozen QDA: Gaussian 0.3011/87.00%; Student-t 0.5266/81.20%.", "idea": "Fractional radial test log-loss/accuracy: Gaussian 0.3014/86.93%; Student-t 0.4285/82.20%. Maximum test radius: Gaussian 24.74; Student-t 84.57. Cholesky-versus-inverse radius error: 4.4e-16." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a 2D synthetic identity embedding and one fixed random seed were tested. UCI data, a learned encoder, warmup scheduling, calibration, parameter/FLOP matching, repeated-seed confidence intervals, and explicit covariance condition-number tracking were not evaluated." }