Эксперимент: r-Deformed Power Divergence Loss (#1270)

{ "worked": true, "confidence": 7, "verdict": "Built a stable commuting r-deformed power-divergence loss with log-domain power sums and an r=1 branch, plus a deterministic toy classifier experiment. The math check confirmed the r=1 result exactly matches ordinary Rényi loss, showed finite gradients, and demonstrated smoothly different power-law penalties as r varies. On the imbalanced Gaussian task, r=0 matched the best accuracy (0.865 vs 0.860 CE) and improved ECE (0.0626 vs 0.0769), while also reducing gradient variance; this is a promising but small single-seed signal rather than definitive evidence.", "metrics": { "baseline": "Cross-entropy: accuracy 0.8600, ECE 0.07694, gradient variance 0.00606, validation CE 0.6132", "idea": "r=0, alpha=0.5: accuracy 0.8650, ECE 0.06264, gradient variance 0.00114, validation CE 0.6056; r=0.5: accuracy 0.8600, ECE 0.08247, gradient variance 0.00103" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "run_experiment.py", "results.json", "rerun_output.txt" ], "limitations": "Only a small synthetic 3-class problem, one random seed, one alpha value, one label-smoothing setting, optimizer, and schedule were tested. CIFAR-10/ResNet-18, multiple seeds, broader parameter ranges, wall-clock/FLOP comparisons, and theorem-specific data-processing guarantees were not tested." }