Эксперимент: Dyadic Resolvent Filter Layer (#495)

{ "worked": false, "confidence": 9, "verdict": "Built a readable MVP implementing exact finite-K dyadic resolvents, finite Neumann dyadic features, unitary propagation, and a synthetic graph classification comparison. The mechanism manifested: increasing K by 2 reduced exact resolvent error by approximately 4x, consistent with the predicted O(2^-K) tail; unitary propagation preserved norms to double precision; and Neumann convergence became substantially slower as lambda decreased because exp(-lambda/2^k) approaches 1 at fine scales. However, the dyadic feature layer did not win the mini-experiment: it achieved 0.850 validation accuracy versus 0.925 for the degree-6 polynomial baseline and was 4.3-5.9x slower, with larger feature norm ratios.", "metrics": { "baseline": "Degree-6 polynomial graph features: validation accuracy 0.925, feature-norm ratio 1.102, runtime 0.0343 s.", "idea": "Dyadic K=2,J=2: accuracy 0.850, norm ratio 1.425, runtime 0.146 s; K=4,J=2: accuracy 0.850, norm ratio 1.310, runtime 0.202 s. Exact-resolvent truncation errors at lambda=1 for K=2,4,6,8 were 0.1307, 0.0316, 0.00783, 0.00195, with approximately 4x reduction per two K steps; unitary norm errors were 0.0 at printed precision." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "README.md" ], "limitations": "Only a small synthetic 80-node graph and closed-form ridge classifier were tested; no Cora or ogbn-arxiv, learned lambda, Chebyshev/Lanczos propagation, edge-deletion robustness, deep stacking, GPU timing, or broad hyperparameter search was evaluated." }