Эксперимент: Biclique-free hierarchical attention (#1195)

{ "worked": true, "confidence": 8, "verdict": "Built dyadic hierarchical-bucket attention with inverted-index candidate generation and greedy K_{2,2} repair. The checks showed exact K_{2,2}-freeness, exhaustive detector agreement on all 3x3 bipartite graphs, and linear edge growth with log-log slope 1.0 versus dense quadratic growth with slope 2.0. At n=256 the repaired mask used 504 edges versus 65,536 dense and 3,784 local edges, but random-feature attention differed substantially from dense attention; language-model quality was not tested.", "metrics": { "baseline": "Dense: 65,536 edges at n=256; growth slope 2.000; Python attention time 0.03539 s/call.", "idea": "Hierarchical plus greedy K_{2,2}-free repair: 504 edges at n=256, 130.0x fewer than dense and 7.51x fewer than local; growth slope 1.000; Python attention time 0.01389 s/call; maximum shared keys 1; relative dense-output error 8.516." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "This is a synthetic NumPy toy experiment, not a trained Transformer or WikiText/C4 perplexity evaluation. The hierarchy is fixed rather than learned, the greedy repair is not asymptotically optimized, and runtime uses an unvectorized Python sparse-attention implementation rather than a production GPU kernel." }