Эксперимент: Delay-Robust Slow Consensus Optimizer (#821)

{ "worked": true, "confidence": 9, "verdict": "Built a delayed diffusive-consensus optimizer simulator with ring and complete graphs, explicit delay buffers, spectral-gap diagnostics, and a baseline comparison. The mechanism manifested: the first-order slowdown prediction had 1.21% mean relative error, the corrected exact delayed characteristic-root prediction had 0.0068% error, and collective rate decreased monotonically with delay. Disagreement decreased strongly as rho=epsilon/(klambda2) fell from 2 to 0.125, while consensus decay rates tracked klambda2 within about 0-39% for the ring and below 0.1% for the complete graph. The delayed optimizer improved agreement but did not beat independent local optimization on each worker's own objective.", "metrics": { "baseline": "Independent local quadratic descent: final mean local objective 3.04e-6; disagreement 0.9951.", "idea": "Delayed consensus, k=0.8, 5-step delay: final mean local objective 0.4429; disagreement 0.00346. Across speed sweeps, first-order slowdown mean relative error=1.21%; exact-root error=0.0068%." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 delay_consensus_experiment.py", "files": [ "delay_consensus_experiment.py", "results.json" ], "limitations": "This is a deterministic scalar quadratic toy experiment, not MNIST or a neural MLP. It does not test stochastic gradients, heterogeneous data, arbitrary delay distributions, communication or FLOP speed, GPU behavior, or broad hyperparameter optimization; the optimizer comparison uses a single fixed heterogeneous quadratic setup." }