Эксперимент: Continued-Fraction Lacunary Features (#1197)

{ "worked": true, "confidence": 8, "verdict": "Built continued-fraction lacunary features using golden-ratio denominators and inverse-square-root scaling, plus a reproducible coordinate-regression benchmark. The recursion matched Fibonacci denominators, the finite-series modulus had a log-log slope of 0.841 consistent with sub-Lipschitz behavior, and the finite derivative bound grew linearly with truncation size. On extrapolation to an unseen coordinate interval, lacunary features achieved RMSE 0.0734 versus 0.9800 for NeRF features and 2.3991 for raw coordinates, showing a clear promising effect in this toy setting.", "metrics": { "baseline": "Raw coordinates: train RMSE 0.0666, extrapolation RMSE 2.3991; NeRF Fourier features: train RMSE 0.00382, extrapolation RMSE 0.9800.", "idea": "Continued-fraction lacunary features: train RMSE 0.01399, extrapolation RMSE 0.07340; input dimension 17 and 5,377 parameters versus NeRF's 16 dimensions and 5,313 parameters." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a 1D synthetic continued-fraction-series target and one train/test interval split were tested. The benchmark did not include random Fourier features, multiple seeds, 2D/image fields, wall-clock comparisons, or a strictly parameter-matched architecture; the regularity estimate uses a finite truncation and finite scale range." }