Эксперимент: Tau-leaped parallel discrete Hamiltonian sampler (#960)

{ "worked": true, "confidence": 8, "verdict": "Built a reproducible tau-leaped categorical Hamiltonian sampler with Gillespie reference dynamics, Bernoulli collision resolution, Poisson identity checks, bias sweeps, and timing comparison. The controlled binary-chain experiment showed abs(endpoint bias)/h approximately 0.0647–0.0715 across h=0.002–0.2, confirming first-order error, and collision probability divided by h^2 approached the predicted q1*q2=0.77 (0.769 at h=0.002). The mechanism manifested, but the scalar implementation provided only 1.41x speedup rather than the claimed 4x; GPU batching was not implemented.", "metrics": { "baseline": "Exact Gillespie: 75.96 paths/s, 1.316 s for 100 paths, 4.45 events/path", "idea": "Tau-leap h=0.05: 106.93 paths/s, 0.935 s for 100 paths, 1.41x speedup, 3.94 events/path; controlled bias/h 0.0647–0.0715; collision p/h^2 0.7686 at h=0.002 vs predicted 0.77" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 controlled_check.py && /home/maxwelhelp/main/bin/python3 tau_leap_experiment.py", "files": [ "tau_leap_experiment.py", "controlled_check.py", "results.json", "controlled_results.json" ], "limitations": "The main sampler is scalar NumPy rather than tensorized CUDA, so GPU utilization and the intended batched GPU throughput were not tested. The high-dimensional endpoint comparison used small replicate counts and showed noisy coordinate TV rather than a robust KL estimate; no MNIST, diffusion model, VAE, or 4x wall-clock benchmark was evaluated." }