Эксперимент: Gaussian Barycentric Constraint Layer (#1400)

{ "worked": false, "confidence": 9, "verdict": "Built a vectorized Gaussian barycentric layer with hard rejection and soft violation weighting, plus a seeded simplex-regression comparison. The interval sanity check supported the claimed Jacobian identity (finite difference 0.4077 vs Cov/delta 0.4089) and firm nonexpansiveness (largest lhs-minus-rhs -0.0466). However, soft weighting improved MSE (0.00135 vs 0.00235 clipping) while substantially violating the simplex, and hard rejection had only 6.25% feasible samples, zero useful gradient, and poor MSE (0.245); the complete promised constrained-training effect was therefore not demonstrated.", "metrics": { "baseline": "Clip-renormalize: MSE 0.00235, max constraint violation 1.2e-7, training time 1.69s; exact simplex projection: MSE 0.00243, violation 1.2e-7, 1.90s.", "idea": "Soft Gaussian barycenter: MSE 0.00135, max violation 0.171, training time 2.70s; hard Gaussian conditioning: MSE 0.245, feasible sample rate 6.25%, gradient norm 0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a tiny synthetic 3-simplex regression task was tested, with one seed and K=32 for the training comparison; K in {8,16,32}, multiple seeds, noisy-input robustness, Jacobian spectral norms, and larger polytopes were not evaluated. The hard simplex predicate used a sum tolerance and is not an exact simplex projection; finite-sample hard rejection is not differentiable through rejection and can have sparse or zero gradients." }