# Methods and Artifacts


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# Methods, provenance, and limitations

Run `python3 reproduce_mfvi_variance.py` from the repository root. The CPU-only script uses NumPy, SciPy, and Matplotlib and writes full problem-level records to `outputs/results.json`, a three-panel evidence figure, and `outputs/SHA256SUMS.txt`. Randomness is fixed by explicit seeds.

Primary source:

- OpenReview paper and discussion: https://openreview.net/forum?id=RG7maF4bGu

The implementation is independent. It constructs randomly rotated anisotropic design matrices, computes the exact posterior and analytic mean-field optimum, evaluates the paper's directional and training-distribution identities, runs premise-changing negative controls, and independently recovers selected optima with numerical KL minimization. It imports no author code or saved author outputs.

The derivations establish the stated Bayesian linear-regression results for arbitrary design matrices under a spherical Gaussian prior. They do not establish an unrestricted theorem for nonlinear neural networks, non-Gaussian likelihoods, or arbitrary variational families. Very small positive margins near the diagonal equality case are expected; raw per-problem margins and condition numbers are retained so numerical proximity to equality is visible rather than discarded.