Эксперимент: Uniformly Mixing Coulomb Particle Bank (#1188)

{ "worked": true, "confidence": 7, "verdict": "Built a NumPy Coulomb-gas Langevin sampler with quadratic confinement, mean-field logarithmic repulsion, collision smoothing, finite-difference verification, autocorrelation estimation, and Gaussian prototype controls. The force identity matched finite differences to 2.1e-12 at the smallest tested step. Particle-radius integrated autocorrelation stayed essentially constant as N increased (76.34, 76.98, 78.50 for N=8,32,128), while Coulomb samples had no dead routes and higher assignment entropy than Gaussian controls, indicating a promising signal for uniform per-particle mixing and coverage. This does not verify the paper’s theorem itself; collective-radius autocorrelation decreased from 59.97 to 40.57.", "metrics": { "baseline": "Gaussian controls N=8/32/128: normalized assignment entropy 0.7275/0.6089/0.5579; dead fraction 0/0.3125/0.7578; median nearest-neighbor distance 2.9588/1.0679/1.2121.", "idea": "Coulomb Langevin N=8/32/128: per-particle radius IAT 76.34/76.98/78.50; normalized assignment entropy 0.9317/0.8970/0.9021; dead fraction 0/0/0; median nearest-neighbor distance 0.6293/0.1978/0.1262." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 coulomb_bank.py", "files": [ "coulomb_bank.py" ], "limitations": "Toy 2D sampler only; no CIFAR, learned prototype map, downstream routing accuracy, FLOP-matched training, multiple-seed confidence intervals, exact singular discretization, or direct verification of the paper’s logarithmic Sobolev constant was tested. Assignment statistics use random 2D Gaussian queries and the Gaussian control uses a manually matched scale, so these are illustrative rather than a full application benchmark." }