Эксперимент: Fractional-memory recurrent state (#1034)

{ "worked": false, "confidence": 9, "verdict": "Built a stable PyTorch fractional-memory layer using positive softmax-weighted exponential states with logarithmically spaced time constants, plus numerical verification scripts. The Mittag-Leffler power-law asymptotic matched the predicted 1/sqrt(pi) constant with relative error falling from 0.49% at lag 100 to 0.00005% at lag 1e6, and exponential stability/half-life predictions matched discrete observations within one step. However, bank approximation error improved strongly from K=1 to K=4 but then saturated rather than continuing to improve, and the fractional K=8 filter had higher random-signal MSE than the best single exponential; therefore the full claimed mechanism was not demonstrated as a win.", "metrics": { "baseline": "Best single exponential: MSE 0.0001200 against the exact normalized fractional filter; delayed impulse at lag 4000: 1.29e-58.", "idea": "Fractional K=8 bank: MSE 0.0006433; delayed impulse at lag 4000: 1.52e-05, approximately 1.17e53 times larger retention than the tau=32 baseline. Relative kernel-fit error by K: 1=101.99, 2=0.818, 4=0.338, 8=0.314, 16=0.313, 32=0.313." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 verify.py", "files": [ "fractional_memory.py", "verify.py", "results.json" ], "limitations": "No trained delayed-copy model, GRU, Transformer, language-model, equal-parameter benchmark, GPU benchmark, or alpha values other than 1/2 were tested. The bank fit used fixed logarithmic time constants and a finite horizon, so improved fitting or learned decays remain unexplored." }