Эксперимент: Persistent Hamiltonian categorical sampler (#959)

{ "worked": true, "confidence": 9, "verdict": "Built a Gillespie persistent-momentum sampler for a uniform categorical ring and numerically checked the skew detailed-balance identity. The predicted sign correlation 2 asin(rho)/pi and run length 1/(1-correlation) matched all five rho values with absolute correlation errors below 0.004. Persistence improved the ring position autocorrelation metric from 187.7 at rho=0 to 151.0 at rho=0.75, but this is only about a 20% improvement, so the mechanism manifested without demonstrating the claimed 2x sampling gain.", "metrics": { "baseline": "rho=0: position_tau=187.72, sign_corr=0.00257", "idea": "rho=0.75: position_tau=150.96, sign_corr=0.53851; predicted sign_corr=0.53989, predicted run_length=2.1734, observed run_length=2.1669" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 sampler_experiment.py", "files": [ "sampler_experiment.py", "results.json" ], "limitations": "Only a uniform one-dimensional ring was tested; no multimodal nonuniform categorical target, Metropolis/Gibbs baseline, batch latent model, FLOP-matched comparison, or high-dimensional token-sequence experiment was evaluated. The continuous-time waiting-time estimate is noisy because Gaussian momentum produces heavy-tailed inverse-rate waits." }