Эксперимент: Prolate Energy-Preserving Bottleneck (#929)

{ "worked": true, "confidence": 8, "verdict": "Built a fixed prolate/DPSS bottleneck with theorem-inspired rank selection, tensor encode/decode, Fourier comparison, and numerical verification. The concentration matrix had eigenvalues in [0,1] up to numerical precision; ceil(asymptotic rank)=44 exactly matched the empirical count above delta=0.1. On band-limited covariance samples at rank 44, DPSS reconstruction error was 0.00108 versus 0.00885 for Fourier and 0.535 for a random subspace, while reducing quadratic attention work by 79.0%. This is a clear toy-signal win, but no trained neural block or language-model perplexity experiment was run.", "metrics": { "baseline": "Fourier rank 44: normalized reconstruction error 0.0088546; random rank 44: 0.5347466; full quadratic work baseline = 1.0", "idea": "Prolate rank 44: normalized reconstruction error 0.0010754, 87.9% lower than Fourier; empirical/asymptotic rank both 44; quadratic work fraction 0.2101 and reduction 79.0%; encode/decode max error 1.11e-15" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 validate.py", "files": [ "prolate_bottleneck.py", "experiment.py", "validate.py", "results.json", "validation_results.json" ], "limitations": "Only a small NumPy toy experiment on synthetic samples from the assumed band-limited covariance was tested. No Transformer, attention memory measurement, wall-clock speed benchmark, learned correction, residual bypass, WikiText/LRA data, or perplexity/accuracy comparison was run; the asymptotic theorem was checked through its rank prediction rather than independently reproving its error bound." }