Эксперимент: Carleman-Lifted Polynomial State Space (#1198)

{ "worked": false, "confidence": 9, "verdict": "Built an exact index-based truncated Carleman lift, a factor-wise N=2 neural cell, and reproducible verification/experiment code. The defect equation was confirmed exactly in the toy ODE with residual RMS 0.0, but the lifted learner reached MSE 0.02917 versus 0.00457 for the GRU on the same synthetic sequence task, so no practical win was observed.", "metrics": { "baseline": "GRU final training MSE: 0.004574526567012072", "idea": "N=2 Carleman lifted cell final training MSE: 0.02916671149432659; toy max lift error: 0.005699823487373749; mean defect norm: 0.004474148873655404; defect-identity residual RMS: 0.0" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 carleman_experiment.py", "files": [ "carleman_experiment.py", "results.json" ], "limitations": "Only a tiny d=2, T=32 synthetic task was tested; no copy-memory, long-range oscillation, WikiText, matched FLOP/parameter study, adaptive order selection, or defect regularization was evaluated. CUDA cuDNN failed in this shared environment, so training fell back to CPU." }