Эксперимент: Complete MLSI Heat Regularization for Matrix Attention (#1175)

{ "worked": false, "confidence": 9, "verdict": "Built a numerical MLSI/BKM verification and a small CUDA toy comparison in experiment.py. The scalar MLSI inequality held, and exact FFT heat flow produced BKM-information ratios below the predicted e^(-2t) bound at every tested time. However, the toy heat variant was slower at about 2.8x and had worse mean MSE and high-frequency residual power across four seeds, so no neural-training win was observed.", "metrics": { "baseline": "Toy denoising: mean MSE 0.0177; mean high-frequency residual power 0.971; about 0.92 seconds/run on CUDA.", "idea": "Toy heat variant: mean MSE 0.0186; mean high-frequency residual power 1.046; about 2.70 seconds/run on CUDA. BKM ratios at t={0.01,0.03,0.06,0.1} were {0.759,0.455,0.233,0.111}, all below bounds {0.980,0.942,0.887,0.819}." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "The training comparison is a tiny synthetic denoising proxy rather than a Transformer, attention router, MoE, or language-model task. The toy objective uses heat-smoothed matrix-derived features but does not add the full differentiable BKM penalty to an attention loss; no entropy-regularization baseline, tau/lambda sweep, matched-FLOP study, or head-collapse metric was tested." }