Эксперимент: Sketch-orthogonal low-rank optimizer updates (#1287)

{ "worked": false, "confidence": 8, "verdict": "Built a NumPy MVP implementing the standard tangent-space projector and sketch-Cholesky factor reconditioning. The math checks confirmed factor-product invariance (2.35e-16 relative error), sketch-orthogonality (7.54e-6 error), and projector normality (9.82e-15), while reducing an intentionally ill-conditioned factor from condition number 8.03e7 to 4.08. In the tiny regression run, sketch and exact QR reached essentially identical loss, but sketch reconditioning was slower than QR (0.308s vs 0.221s) and did not provide Euclidean orthogonality; therefore no optimization win was observed.", "metrics": { "baseline": "No reconditioning: final loss 0.5339387, U orthogonality error 0.0577, runtime 0.0579s.", "idea": "Sketch-Cholesky: final loss 0.5339349, U orthogonality error 12.436 (sketch Gram error 7.54e-6), factor condition numbers U/V 5.08/5.03, runtime 0.3078s. Exact QR control had the same loss 0.5339349, U orthogonality 8.76e-16, and runtime 0.2213s." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "This is a small dense CPU NumPy regression benchmark, not a Transformer or distributed communication test. The sketch uses s=r+8 rows and is not expected to preserve Euclidean orthogonality as well as a full QR; only sketch-orthogonality and conditioning were evaluated. No GPU, memory, multi-seed, wall-clock scaling, or downstream validation-accuracy experiment was tested." }