Эксперимент: Work-trained neural Hamiltonian bridge (#407)

{ "worked": true, "confidence": 8, "verdict": "Implemented a reparameterized neural Hamiltonian-style bridge and an exact Gaussian path-law sanity check. The mechanism manifested: mean work scaled quadratically with displacement (observed slope 0.5366 versus predicted 0.5346, 0.36% error), the endpoint/path KL ratio matched 0.9352, and the endpoint KL bound held with zero violation. In the double-well mini-experiment, training reduced mean work and energy versus the uncorrected proposal, but work variance remained very large and the training loss was not consistently decreasing, so this is mechanism validation rather than a robust sampler win.", "metrics": { "baseline": "Uncorrected double-well proposal: work mean 76.19, work std 1562.43, mode-positive fraction 0.5016, mean energy 2.5473.", "idea": "Work-trained bridge: work mean 12.33, work std 201.38, mode-positive fraction 0.4929, mean energy 1.2871. Exact checks: quadratic slope 0.5366 observed versus 0.5346 predicted; endpoint/path KL ratio 0.9352 observed versus 0.9352 predicted; maximum endpoint-bound violation 0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py > results.json && cat results.json", "files": [ "experiment.py", "results.json" ], "limitations": "The path/reference construction is a small toy approximation rather than an exactly reversible Hamiltonian target path law. Only a 2-D double-well was used for the sampler comparison; HMC, Gaussian-mixture experiments, MMD, effective sample size, and longer stability or mode-mixing studies were not tested. Work variance remained high and optimization was not monotonic." }