Эксперимент: Variance-aware gradient reduction trees (#446)

{ "worked": true, "confidence": 9, "verdict": "Built a readable toy implementation of balanced, sequential, and variance-aware Huffman reduction trees with common-ancestor kernels and predicted costs. The mechanism manifested: the exact expectation identity matched Monte Carlo within 0.66%, roundoff MSE scaled as u^1.999 versus the predicted u^2, and for variance ratio 16 the balanced cost was 69.0 versus 43.0 for Huffman, confirmed empirically as 68.62 versus 42.86. This is a promising math-level signal, but not evidence of end-to-end distributed-training throughput or accuracy improvement.", "metrics": { "baseline": "Balanced tree: heterogeneous variance-16 predicted cost 69.0, observed 68.62; equal-variance cost 24.0.", "idea": "Huffman variance-aware tree: heterogeneous variance-16 predicted cost 43.0, observed 42.86, a 37.7% predicted reduction and 37.4% observed reduction; gain increased from 0% at ratio 1 to 57.3% at ratio 64. Roundoff log-log slope was 1.999 versus predicted 2.0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "run_experiment.py", "results.json", "experiment_output.txt" ], "limitations": "Only a CPU toy Monte Carlo study was tested. It uses Gaussian additive local-roundoff noise rather than actual BF16/FP16 hardware arithmetic, and does not implement distributed communication, chunk-statistic estimation, adaptive refresh, hardware fan-in constraints, optimizer training, throughput, overflow rates, or final model accuracy." }