Эксперимент: Convex Bayesian Potential Head (#1313)

{ "worked": true, "confidence": 9, "verdict": "Built a finite-state Bayesian inverse-problem MVP with an exact partition function, frozen neural features, a convex linear potential head, covariance Hessian/Newton optimization, and an unconstrained neural-score baseline. The Hessian was PSD with minimum eigenvalue 0.00588, and the finite-difference Hessian-vector check matched to 2.3e-11. Across five initializations, the convex head converged to the same objective and posterior, with better held-out objective and KL and essentially zero seed variance than the neural baseline; this is a clear toy-level signal, not evidence of broad superiority.", "metrics": { "baseline": "Unconstrained neural score: held-out objective -0.3595 +/- 0.0363, posterior KL 0.1760 +/- 0.0221, expected 90% coverage 0.9449 +/- 0.0034 across 5 seeds.", "idea": "Convex potential head: held-out objective -0.5237 +/- 1.5e-13, posterior KL 0.0910 +/- 1.0e-13, expected 90% coverage 0.9616 +/- 0.0000 across 5 initializations; training objective -0.613880 in every run." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "run.log" ], "limitations": "Only a five-state one-dimensional latent toy problem was tested, with an exact finite prior rather than sampled particles. The feature map was frozen, the baseline had a different parameterization and was trained with a fixed Adam schedule, and no continuous high-dimensional inverse problem, GPU path, wall-clock comparison, intermittent feature unfreezing, or large-scale calibration study was evaluated." }