Эксперимент: Dyadic Hankel Boundary Attention (#516)

{ "worked": true, "confidence": 8, "verdict": "Built a reproducible dyadic Hankel MVP in dyadic_hankel.py with cached thin-SVD application and quantitative checks. Across h=4..64, every tested normalized singular value satisfied the predicted s_(N+1) <= 4^-N bound; observed ranks were 2,3,3 for eps=1e-2,1e-3,1e-4 versus conservative bounds 4,5,7 and remained independent of h. Rank-4 factorization produced about 1e-6 relative output error and measured speedups of 2.1x-11.5x as block size grew, confirming the mechanism but not a full language-model win.", "metrics": { "baseline": "Dense H@V: 0.077-1.568 ms for h=64-512; relative error 0 by definition; arithmetic cost ratio versus rank-4 factorization is 12.8x-102.4x.", "idea": "Rank-4 cached factorization: 0.036-0.137 ms, relative output error 1.0e-6-1.9e-6, measured speedup 2.12x-11.46x. Singular-bound checks passed 25/25; observed ranks for eps=(1e-2,1e-3,1e-4) were (2,3,3) at every h." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 dyadic_hankel.py", "files": [ "dyadic_hankel.py", "results.json", "run_output.txt" ], "limitations": "Only a CPU toy discretization of one relative-position Hankel cross-block was tested. No learned gates, reverse-direction integration, multi-block attention, GPU kernel implementation, Transformer training, perplexity, KV-cache memory, or context lengths beyond the toy block sizes were evaluated; timing is sensitive to BLAS and allocation effects." }