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name: annealed_langevin_sampler description: Run annealed Langevin dynamics with composed scores for F-NPSE or PF-NPSE posterior sampling.

Annealed Langevin Sampler

Use this skill when a recovery needs to sample from a posterior approximation using a score function already composed from F-NPSE or PF-NPSE terms. It implements the paper's Algorithm 1 in a bounded, deterministic-seeded form suitable for tests and recovery harnesses.

Do not use this skill to train score networks or to define the F-NPSE algebra. It consumes a callable score and a reference sampler.

Inputs

• Initial samples from the high-noise reference distribution, or a reference sampler.
• Composed score callable score(theta, t).
• Time levels ordered from high noise to low noise.
• Step size, Langevin steps per level, and random seed.

Outputs

• Final posterior samples.
• Trace metadata with score norms, sample means, level count, step size, and seed.

Workflow

1. Initialize samples from the reference distribution.
2. Traverse time levels from high noise to low noise.
3. Apply theta <- theta + 0.5 * step_size * score(theta, t) + sqrt(step_size) * noise.
4. Log per-level summary statistics.
5. Return samples and trace.

Validation

Run:

python /share/project/yuyang/workspace/Paper2Skills/Distiller/skills/module-to-skill/scripts/validate_skill_tree.py <skill_dir> --run-tests

The tests use an exact Gaussian score and verify that samples move toward the target mean while preserving trace metadata.

Limitations

The sampler is sensitive to step size and score scaling. Recovery scripts should expose these settings and avoid interpreting a short bounded run as a full-scale reproduction of the paper's 400-level experiments.