Эксперимент: Order-Adaptive Integral Optimizer (#1151)

{ "worked": true, "confidence": 7, "verdict": "Built a PyTorch order-adaptive integral optimizer with lazy nested states, EMA residual-triggered order growth, gain ramping, and state clipping. The quadratic check verified the coefficient inequality and stable continuous-time polynomial roots; on slow quadratics, order transitions reproducibly occurred and reduced final loss versus SGD, for example 0.0002374 versus 0.0002991 on curvature [1, 0.01]. The effect was absent on easy and rapidly solved cases, and the MLP smoke test matched SGD, so this is a promising toy signal rather than a demonstrated general training win.", "metrics": { "baseline": "Slow quadratic [1, 0.01], 2000 steps: final loss 2.9912e-4; [1, 0.1]: 8.1569e-5. Easy [1,2,4], 1200 steps: 2.5314e-17.", "idea": "Slow quadratic [1, 0.01], 2000 steps: final loss 2.3742e-4 with p=1 at step 30 and p=2 at step 50; [1, 0.1]: 6.7628e-5. Easy [1,2,4]: unchanged at 2.5314e-17 and remained p=0. MLP smoke test: identical to SGD, final loss 0.04702." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "order_adaptive.py", "run_experiment.py", "results.json" ], "limitations": "The mini-experiment used deterministic quadratic systems and one tiny synthetic MLP only; MNIST, Penn Treebank, delayed stochastic gradients, fixed higher-order baselines, wall-clock speed, memory overhead, and broad seed sweeps were not tested. The slow-quadratic probe was run interactively and its summary is not separately stored in results.json." }