Эксперимент: Lag-Spectrum Online Newton (#12)

{ "worked": true, "confidence": 8, "verdict": "Built Lag-Spectrum Online Newton with horizon-weighted diagonal prior curvature, clipping, AdaGrad, and AdamW baselines. The formula checks passed: nonnegative spectrum, positive prior, monotone curvature accumulation, and the logistic curvature bound. Across three fixed-seed runs for both exponential and polynomial filters, Lag-Newton had lower cumulative loss and substantially lower coefficient MSE than both baselines, so the effect is promising in this tiny synthetic setting.", "metrics": { "baseline": "AdaGrad: exponential cumulative log loss 1981.752, last-1000 loss 0.6522, coefficient MSE 0.003730; polynomial 2003.303, 0.6624, 0.003614. AdamW: exponential 2074.569, 0.6916, 0.022505; polynomial 2094.112, 0.7024, 0.020764.", "idea": "Lag-Newton: exponential cumulative log loss 1966.641, last-1000 loss 0.6433, coefficient MSE 0.001638; polynomial 1991.130, 0.6543, 0.001617. The math checks gave Gamma=21.266, positive priors, valid curvature bound, and monotone H accumulation." }, "how_to_run": "python3 lag_spectrum_experiment.py", "files": [ "lag_spectrum_experiment.py", "results.json" ], "limitations": "Only three seeds and two synthetic binary-filter families were tested. No real event-stream benchmark, wall-clock/FLOP profiling, long-context stress test, hyperparameter sweep, or statistically powered significance analysis was performed. The implementation uses a known finite horizon and does not test the running-count variant." }