Эксперимент: Fractional Memory State-Space Layer (#1119)

{ "worked": true, "confidence": 8, "verdict": "Built a positive, logarithmically spaced exponential-state approximation of the fractional relative-history operator, with NNLS-fitted weights, exact stable discretization, transfer analysis, and a delayed-retrieval toy benchmark. Mechanism checks confirmed power-law impulse slopes (errors 0.0002, 0.0020, and 0.0243 for p=0.2, 0.5, and 0.8) and fractional transfer phase/slope, especially at p=0.5 and 0.8. The retrieval MSE was essentially unchanged versus the matched exponential and raw baselines, so the mechanism manifested but a practical learning win was not demonstrated.", "metrics": { "baseline": "Matched single exponential retrieval MSE 0.97813; raw input MSE 0.97788.", "idea": "Fractional 16-mode bank retrieval MSE 0.97792. Impulse log-slope observed/predicted: p=.2 -0.800/-0.800, p=.5 -0.502/-0.500, p=.8 -0.176/-0.200. Transfer phase observed/predicted: p=.2 -0.509/-0.314 rad, p=.5 -0.838/-0.785 rad, p=.8 -1.275/-1.257 rad. Stability spectral radii exactly matched exp(-lambda_min*dt) for dt=.1,1,4." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 fractional_memory_experiment.py", "files": [ "fractional_memory_experiment.py", "results.json", "run_output.txt" ], "limitations": "Only a NumPy/SciPy toy verification and a small isolated-pulse delayed-retrieval benchmark were tested; no trained GRU/SSM neural model, equal-parameter FLOP accounting, LRA task, learned p/rates, noise robustness, or extrapolation study was performed. The p=0.2 transfer approximation showed noticeable finite-bank phase and slope error." }