Эксперимент: Matroid-selected circular latent coordinates (#1393)

{ "worked": false, "confidence": 9, "verdict": "Built wrapped edge-cochain Gram estimation, energy-ordered vector-matroid selection, persistent-direction residuals, and a torus autoencoder comparison. The residual behaved as claimed: approximately 0 when both directions were retained and approximately 1 when one was omitted; circular coordinates also recovered their angles essentially exactly. However, minimum-energy selection chose a distractor plus a mixed coordinate, and the fixed circular representation had substantially worse reconstruction than the learned 2-scalar baseline, so no overall representation win was observed.", "metrics": { "baseline": "2-scalar learned autoencoder reconstruction MSE 0.10022 after 1000 steps", "idea": "Selected sine/cosine coordinates reconstruction MSE 0.48458; angle mean wrapped error 2.49e-17; full residual 4.52e-16 versus omitted-direction residual 1.00000" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "clean_check.py", "results.json" ], "limitations": "Only a small synthetic torus and one random seed were tested. The circular decoder used fixed dictionary coordinates while the baseline learned its encoder, and no VAE, prediction loss, multiple seeds, or persistent-cohomology estimator was evaluated. The experiment also revealed that the stated energy ranking can favor a low-energy distractor unless the candidate dictionary and projected metric are carefully calibrated." }