Эксперимент: Finite-Horizon Walk Reciprocity Control (#1189)

{ "worked": true, "confidence": 8, "verdict": "Built an exact finite-horizon reciprocity diagnostic, differentiable walk-energy regularizer, nilpotent sanity check, and three-seed toy regression comparison. A strictly triangular nilpotent matrix had spectral radius 0 and A^n=0, yet substantial positive finite-horizon walk energy (3.664), while a symmetric control had approximately zero energy; iterative powers matched exact powers to 1.1e-16. The regularizer reduced walk energy in all three seeds, but did not reliably improve loss and increased mean gradient norm, so a practical training win is not established.", "metrics": { "baseline": "Mean last-50-step MSE 0.01595, walk energy 0.84470, gradient norm 0.00448 across seeds 7, 19, 31.", "idea": "Mean last-50-step MSE 0.01738, walk energy 0.80027, gradient norm 0.00518; walk energy decreased in all seeds, while loss improved in only 1/3 seeds." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 walk_reciprocity_experiment.py", "files": [ "walk_reciprocity_experiment.py", "results.json" ], "limitations": "Only a tiny synthetic full-batch regression task and three seeds were tested; no CIFAR-10, Transformer, GNN, spectral-norm baseline, Hutchinson estimator, validation split, FLOP-normalized comparison, or broad hyperparameter sweep was evaluated. The target was calibrated from each seed's baseline final-window energy rather than a separately measured first-epoch median." }