# Эксперимент: Exact Moment Message Passing (#990)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built an exact 2D tensor-product polynomial moment contraction MVP and numerically verified the core identity. Across p=1..4, direct and moment outputs matched to <=8.5e-14 absolute error; the predicted occupancy crossover was observed at sampled k=8,16,32 for monomial counts 4,9,16, and measured speedups at k=512 were 30.0x, 11.7x, and 11.2x for p=1,2,3. The mechanism is real, though the benchmark uses a deliberately polynomial kernel and NumPy overhead rather than a full neural point-cloud layer.",
  "metrics": {
    "baseline": "Direct particle-query evaluation: O(kQ); at occupancy 512, timings were approximately 20.9 ms (p=1), 11.0 ms (p=2), and 12.4 ms (p=3).",
    "idea": "Exact moment contraction: O((p+1)^2(k+Q)); at occupancy 512, measured speedups were 30.0x (p=1), 11.7x (p=2), and 11.2x (p=3), with max relative error below 1.6e-15."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 moment_experiment.py",
  "files": [
    "moment_experiment.py",
    "results.json"
  ],
  "limitations": "Did not test a learned neural layer, sparse hierarchy construction, multiple occupied boxes, compact-support non-polynomial kernels, GPU kernels, batching, or realistic end-to-end PointNet/graph workloads. Timing at low occupancy is dominated by Python/NumPy overhead and is noisy."
}