Эксперимент: Cholesky-Structured SPD Classifier (#457)

{ "worked": true, "confidence": 8, "verdict": "Built a Cholesky-structured SPD classifier with automatic positive-definiteness, triangular tangent terms, and matrix-power logits in experiment.py. The mechanism checks matched the predictions: Cholesky reconstruction error was 8.9e-16, all factor-generated matrices had positive minimum eigenvalues, and both the power expansion error and scaled-power limit error decreased approximately linearly when theta was halved. On the synthetic task, the structured head and log-Euclidean baseline both reached 100% accuracy; the structured head had lower final loss (0.0638 vs 0.2670) but was substantially slower (1.58s vs 0.044s), so no speedup was observed.", "metrics": { "baseline": "Log-Euclidean prototype classifier: accuracy 1.000, cross-entropy 0.2670, runtime 0.0436 s", "idea": "Cholesky-structured head: accuracy 1.000, cross-entropy 0.0638, runtime 1.5751 s; reconstruction error 8.9e-16; minimum generated-factor eigenvalues 8.5e-05 to 3.9e-04; scaled-power limit error decreased from 0.01705 at theta=0.4 to 0.000979 at theta=0.025" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py" ], "limitations": "The experiment used small synthetic covariance matrices, M=I, full-batch optimization, and eigendecomposition for matrix powers, so it does not validate the proposed speed advantage of a genuinely Cholesky-only power/operator implementation. It did not test CIFAR-10, activity data, dimensions up to 128, minibatch throughput, peak memory, or repeated Lyapunov solves." }