Эксперимент: Cone Bi-Rayleigh Stability Regularizer (#1248)

{ "worked": false, "confidence": 8, "verdict": "Built a cone bi-Rayleigh quotient regularizer prototype and verified the core math numerically: at a positive right/left eigenpair, the quotient matched 1−mu to 2.6e-12, and alternating positive probe updates reduced the joint residual by about 1e24x. In the RNN mini-experiment, cone regularization improved mean test loss over vanilla (0.0306 vs 0.0867) but was substantially slower (18.0s vs 8.4s) and clearly worse than spectral regularization (0.00410 test loss, 10.6s); therefore it did not demonstrate a win over the standard control.", "metrics": { "baseline": "Mean test MSE 0.08671; mean runtime 8.44s", "idea": "Mean test MSE 0.03056; mean runtime 17.97s; mean estimated mu -0.8025; math quotient absolute error 2.57e-12; probe residual ratio 1.09e-24", "spectral_control": "Mean test MSE 0.00410; mean runtime 10.62s" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "The mini-task was a small delayed-output toy rather than the requested adding/copy-memory benchmarks, used a materialized recurrent matrix instead of true JVP/VJP calls, did not measure exploding-gradient frequency or matched FLOPs, and used only three seeds. The cone penalty was often nearly inactive because the estimated growth eigenvalue was below the threshold." }