Flow Pocket Lab

Verified project card

# Flow Pocket

Flow Pocket trains an exactly invertible RealNVP density model on a curved
five-armed pinwheel distribution. Eight affine coupling layers transform data into
a standard Gaussian while tracking the exact change-of-variables log determinant.

The benchmark compares held-out negative log-likelihood and generated-sample MMD
against a fitted full-covariance Gaussian and a five-component Gaussian mixture.
It also measures forward/inverse cycle error to verify that the saved neural
transform is numerically invertible.

## Verified results

The flow trained on 40,000 samples and was evaluated on 10,000 independently
generated samples.

| Model | Held-out NLL | Sample MMD |
| --- | ---: | ---: |
| RealNVP | 2.2629 | 0.000236 |
| Five-component GMM | 2.5887 | 0.000436 |
| Full-covariance Gaussian | 3.3527 | 0.002800 |

The eight-coupling-layer RealNVP has 21,536 parameters. Its maximum absolute
forward/inverse reconstruction error over 2,000 held-out points was `5.78e-6`.
MMD uses independently randomized 1,000-sample subsets and a shared median
distance bandwidth.

## Reproduce

```powershell
uv run python projects/flow-pocket/train.py
```

Evaluation snapshot

{
  "benchmark": "Five-arm pinwheel density estimation",
  "training_examples": 40000,
  "heldout_examples": 10000,
  "results": {
    "realnvp": {
      "parameters": 21536,
      "test_nll": 2.2628610134124756,
      "sample_mmd": 0.00023621320724487305,
      "maximum_cycle_error": 5.781650543212891e-06
    },
    "full_covariance_gaussian": {
      "test_nll": 3.352746780780259,
      "sample_mmd": 0.002799742898649704
    },
    "five_component_gmm": {
      "test_nll": 2.5887062549591064,
      "sample_mmd": 0.00043558339810489954
    }
  },
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}

Backed-up artifact tree

• README.md
• __pycache__/app.cpython-311.pyc
• __pycache__/data.cpython-311.pyc
• __pycache__/model.cpython-311.pyc
• app.py
• artifacts/flow-pocket/classical_controls.joblib
• artifacts/flow-pocket/evaluation.json
• artifacts/flow-pocket/generated_samples.npz
• artifacts/flow-pocket/realnvp.safetensors
• data.py
• data/pinwheel_test.parquet
• model.py
• requirements.txt
• train.py