Эксперимент: Reversible Matrix Cluster Layer (#1239)

{ "worked": true, "confidence": 7, "verdict": "Built a small SPD matrix-cluster layer with ordered quiver products, eigendecomposition-based square roots, and a CUDA-capable synthetic training comparison. Mutation followed by the same mutation reconstructed the original state to 5.8e-16 relative error on the supplied three-node quiver and 2.0e-15 on a noncommuting four-node probe; the latter also showed 0.467 relative nonsymmetry in the ordered product, confirming that symmetrization is needed. On one fixed synthetic relational regression task, the matrix layer reached MSE 0.0614 versus 0.0772 for an equal-parameter residual baseline, which is promising but preliminary.", "metrics": { "baseline": "Final synthetic regression MSE 0.0772172; 449 parameters; checkpoints 7.1784, 0.2423, 0.1319, 0.0779", "idea": "Final synthetic regression MSE 0.0613694; 449 parameters; checkpoints 5.2954, 0.3482, 0.1652, 0.0624; inverse relative error <=5.8e-16 on the three-node test and 1.98e-15 on the four-node test" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only one small synthetic regression task and one random seed were tested; no molecular or OGB benchmark, FLOP profiling, multi-seed confidence interval, gradient-variance comparison, or long-horizon stability study was performed. The noncommuting branch symmetrizes M before eigendecomposition, so this is an engineering adaptation rather than a literal noncommutative exchange relation." }