Эксперимент: Cubic-Rate Third-Order Langevin Optimizer (#487)

{ "worked": true, "confidence": 9, "verdict": "Built a PyTorch third-order Langevin optimizer with velocity and acceleration states, acceleration-only Gaussian noise, cubic-rate solver, and optional curvature-based step-size limiting. The mechanism checks succeeded: measured unstable rates matched the cubic root within 0.04%, curvature-scaling slopes matched (0.33730 observed vs 0.33720 predicted), rates increased monotonically with negative curvature, and dt·r≈0.2 produced only 5.66% rate error. The optimizer did not win the toy MLP benchmark: momentum reached loss 0.0516 versus 1.7160 for third-order Langevin after 300 steps.", "metrics": { "baseline": "Momentum SGD: final loss 0.0516, accuracy 99.17%, 0.529 seconds; plain SGD: final loss 0.2256, accuracy 94.34%.", "idea": "Third-order Langevin: final loss 1.7160, accuracy 51.32%, 1.030 seconds. Mechanism: fixed-rate relative error 0.034%; observed versus predicted scaling slope 0.33730 versus 0.33720; dt*r=0.197 yielded 5.66% rate error." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 verify_cubic_langevin.py && /home/maxwelhelp/main/bin/python3 benchmark_mlp.py", "files": [ "verify_cubic_langevin.py", "third_order_optimizer.py", "benchmark_mlp.py", "results.json", "benchmark_results.json" ], "limitations": "Only a scalar linearized saddle and one small synthetic full-batch MLP were tested; no 20-seed study, minibatch training, CIFAR-10, Hessian-vector-product curvature estimator, adaptive damping controller, sampling-distribution validation, or systematic hyperparameter tuning was performed." }