# Эксперимент: Affine-symmetry-free GMM latent prior (#580)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a differentiable affine-signature separation penalty, an affine-residual estimator, and a small mixture-prior latent autoencoder experiment in experiment.py. The toy stationary-distance prediction matched observations to about 3e-7 across eta values, and increasing epsilon increased separation as predicted. Regularization increased the measured affine residual from 0.512 to 7.317, but worsened reconstruction MSE and mixture NLL, so the mechanism worked while the overall tiny-task utility was not demonstrated.",
  "metrics": {
    "baseline": "Toy eta distances: 0.39472148, 0.96468657, 1.71548712, 2.63753772, 3.51303458 for eta=0.03, 0.1, 0.3, 1.0, 3.0; predicted values matched within 3e-7. Mini reconstruction MSE=0.003588, mixture NLL=0.5015, affine residual=0.5118.",
    "idea": "Toy epsilon distances: 2.3607, 2.4981, 2.6375, 2.8504, 3.1403 for epsilon=0.1, 0.3, 0.5, 0.8, 1.2. Mini reconstruction MSE=0.004398, mixture NLL=2.3799, affine residual=7.317."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "The experiment used a tiny synthetic 2D autoencoder rather than dSprites or MNIST, one random seed, and no factor-probe, mutual-information, or multi-seed latent-alignment evaluation. It did not establish a VAE ELBO win. Coincident components require an infinitesimal initialization perturbation because they form an exact zero-gradient stationary point."
}