Эксперимент: State-Dependent Temperature Langevin (#1116)

{ "worked": true, "confidence": 8, "verdict": "Built a state-dependent-temperature Langevin sampler for a Student-t target, including the divergence correction ∇σ² and a matched uncorrected baseline. The mechanism checks confirmed the predictions: stationary-current residual was exactly 0 across α, σ(1) had predicted slope 0.69314718 with 5e-9 maximum error, and the quadratic correction coefficient at x=2 was 0.73240819 observed versus 0.73240819 predicted, with finite-difference error 1.5e-10. The corrected sampler preserved the target variance across α (1.641–1.673 versus the exact 1.667), while the uncorrected sampler became increasingly biased (variance 1.078, 0.817, and 0.583 for α=0.5,1,2); however, no reliable ESS-per-gradient improvement was demonstrated.", "metrics": { "baseline": "Uncorrected state-dependent-noise Langevin: second moment at α=0.5/1/2 = 1.078/0.817/0.583; ESS per gradient = 0.168/0.152/0.168.", "idea": "Divergence-corrected sampler: second moment at α=0.5/1/2 = 1.673/1.641/1.656 versus exact 1.667; ESS per gradient = 0.168/0.150/0.168. Mechanism predictions: max current residual 0, sigma slope error 5e-9, quadratic-coefficient error 9.7e-10." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "rerun_output.txt" ], "limitations": "Only a one-dimensional Student-t target and Euler-Maruyama discretization were tested; no MALA correction, high-dimensional target, neural energy, latent posterior, wall-clock benchmark, or robust long-chain autocorrelation analysis was included. The simple batch-means ESS estimate saturates at the independent-sample ceiling for several settings, so it should not be interpreted as evidence of a sampling-speed win." }