Эксперимент: Moment-preserving HT compression (#1266)

{ "worked": true, "confidence": 9, "verdict": "Built a self-contained moment-preserving low-rank compression experiment in moment_ht_experiment.py. The projection preserved all four moments to about 1.7e-12 over 200 recurrent steps, while ordinary rank-2 compression accumulated moment drift of 5.55 in L2; the minimum-norm sanity check also passed. However, at equal rank the correction increased the factor-storage upper bound from 130 to 390 units and slightly worsened state error, so this demonstrates the stability/conservation benefit but not a memory win.", "metrics": { "baseline": "Rank-2 SVD: final/max moment drift 5.5521/5.6136 L2; mean relative state error 0.30415; factor storage 130 units.", "idea": "Rank-2 SVD plus four-moment correction: final/max moment drift 1.262e-12/1.673e-12 L2; mean relative state error 0.30760; factor-storage upper bound 390 units." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 moment_ht_experiment.py", "files": [ "moment_ht_experiment.py" ], "limitations": "Only a small 32x32 synthetic recurrent system was tested, using matrix SVD as a 2D Tucker analogue rather than a full hierarchical-Tucker implementation. No task-loss benchmark, GPU test, runtime benchmark, second-rank sweep, or recompression of the correction back to a compact rank was performed; the reported idea storage is an upper bound for storing the correction as four additional rank-one terms." }