Эксперимент: Sphere-Jacobian Performative Optimizer (#568)

{ "worked": false, "confidence": 9, "verdict": "Built a self-contained NumPy implementation of sphere-direction paired-rollout Jacobian estimation and a toy performative optimizer comparison in experiment.py. The predicted 1/b_sp scaling was strongly confirmed (log-log slope -1.003), and rollout-noise scaling was approximately confirmed (slope -0.901 versus -1). However, the finite-difference delta sweep did not show the required delta^4 MSE scaling (observed slope -0.015), and the proposed optimizer did not beat SGD in the toy comparison, so the strict mechanism-success criterion is not met.", "metrics": { "baseline": "SGD final performative loss 0.0000420; loss at step 20 0.03284", "idea": "Sphere-Jacobian final performative loss 0.02279; loss at step 20 0.15432; Jacobian MSE slopes: -1.003 versus b_sp and -0.901 versus b_min; delta slope -0.015 versus predicted +4" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a low-dimensional synthetic NumPy environment was tested; no neural network, black-box learned surrogate for g_beta, real dataset, projection constraint, CUDA path, or matched wall-clock/FLOP evaluation was tested. The delta-bias experiment remained dominated by sphere-sampling or model-scale effects despite increasing the direction batch, so the stated delta^4 prediction was not cleanly isolated." }