Эксперимент: Schur Interaction Monitor for Adaptive Hyperparameters (#1357)

{ "worked": true, "confidence": 8, "verdict": "Built a readable Schur interaction monitor implementing R=Gᵀ(H+λI)⁻¹G and the trust update (I+βR)⁻¹. The finite-difference reduced-Hessian check matched −GᵀH⁻¹G with maximum absolute error 1.07e-8, and all measured R eigenvalues were nonnegative. In the shared-noise toy control, Schur updates reduced final loss from 1.794e-4 to 1.231e-4, mean final-10 loss from 1.083e-4 to 5.476e-5, and loss spikes from 36 to 34; this is a promising but not yet neural-network-level win.", "metrics": { "baseline": "Toy quadratic controller: final_loss=0.0001794, best_loss=6.575e-7, mean_last10=0.0001083, loss_spikes=36, max_u_norm=1.4389", "idea": "Schur trust controller: final_loss=0.0001231, best_loss=1.655e-7, mean_last10=5.476e-5, loss_spikes=34, max_u_norm=1.4379; R eigenvalues=[0.0441, 54.0]" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 schur_monitor_experiment.py", "files": [ "schur_monitor_experiment.py", "results.json" ], "limitations": "The experiment is an analytic two-mechanism quadratic controller rather than a CIFAR/Transformer training run. It does not test stochastic minibatch hypergradients, one-step unrolling, runtime/FLOPs, clipping behavior under real optimizer states, or generalization; the spike count is also sensitive to injected noise near the quadratic optimum." }