Эксперимент: Minkowski-Additive Convex Latents (#1203)

{ "worked": true, "confidence": 8, "verdict": "Built a NumPy MVP for direction-indexed convex latents with componentwise nonnegative Minkowski addition, scaling, convex-hull decoding, and Hausdorff evaluation. Across 300 trials, additive and scaling support identities had zero measured error, while convexification had maximum perturbation ratio 1.0, confirming the claimed nonexpansiveness. In chain tests of length 2–10, structured addition was 7.5–19.5x faster than repeatedly forming pairwise vertex sums and hulls, although finite-direction decoding introduced nonzero approximation error that reached about 0.13 in the longest test.", "metrics": { "baseline": "Generic pairwise convex-hull Minkowski composition; chain output size grew from 8 to 51 vertices.", "idea": "Tuple composition; median 12.8x runtime speedup. Maximum additive/scaling identity error was 0.0, maximum convexification Lipschitz ratio was 1.0, and longest-chain decoded Hausdorff error was 0.1307." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 minkowski_latents.py", "files": [ "minkowski_latents.py", "results.json" ], "limitations": "Only small 2D random polygons were tested. No learned predictor, projected-gradient margin enforcement, 3D experiment, GPU benchmark, or MLP baseline was included. The generic baseline computes exact hull-based sums, while the structured method uses a finite direction set and trades exactness for speed." }