Эксперимент: Context-free denoiser with analytic quadratic score injection (#461)

{ "worked": true, "confidence": 8, "verdict": "Built a residual double-well denoiser with inference-time quadratic score injection, including naive -Ky and matched Gaussian -k y/(1+k sigma^2) variants. The mechanism checks passed: predicted Gaussian score coefficients matched measured values to numerical precision (for example k=4,sigma=.7: 1.35135 vs 1.35135), and the Euler OU stability boundary appeared at dt·k=2.1 while dt·k=1.8 remained stable, with observed variances close to theory. In the toy sampler, analytic transfer was competitive with separately trained models (KL 0.373 vs 0.379 at k=2), but was worse at k=.5 (0.579 matched / 0.595 naive vs 0.566 separate), so this is a mechanism validation rather than a demonstrated universal quality win.", "metrics": { "baseline": "Separately trained denoiser: k=0.5 KL=0.5660, covariance=0.7533; k=2.0 KL=0.3789, covariance=0.3840.", "idea": "Shared residual denoiser with naive analytic injection: k=0.5 KL=0.5948, covariance=0.7354; k=2.0 KL=0.3733, covariance=0.4358. Matched Gaussian injection: k=0.5 KL=0.5796, covariance=0.7345; k=2.0 KL=0.3955, covariance=0.4714. Reference covariances were 0.8425 and 0.4794 respectively." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a 2D double-well, one residual potential, two scalar quadratic contexts, one fixed noise-level sampling setup, and small MLPs were tested. No ring-polymer matrix-free implementation, nullspace handling, temperature/mass/boundary sweep, uncertainty calibration, FLOP-normalized training comparison, or high-dimensional diffusion schedule was evaluated; the reference and denoiser training chains are also approximate." }