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name: factorized_score_composition description: Compose F-NPSE and PF-NPSE posterior scores from learned score terms and prior corrections for SBI.

Factorized Score Composition

Use this skill when implementing the central compositional step from F-NPSE or PF-NPSE. It turns score estimates for individual observations or small observation groups into one score for a multi-observation posterior approximation.

Do not use this skill for denoising score training or for sampling. It expects a score predictor to already exist and returns a composed score that a sampler can consume.

Inputs

• Current theta.
• Time index t and total diffusion levels T.
• Observations for F-NPSE or groups for PF-NPSE.
• Prior score function, such as -theta for a standard normal prior.
• Score predictor for one observation or one group.

Outputs

• Composed score vector.
• Metadata with method, observation count, group count, and prior coefficient.
• Per-term score diagnostics that can be logged for recovery evidence.

Workflow

For F-NPSE, compute:

((1 - n) * (T - t) / T) * grad_log_prior(theta) + sum_j s(theta, t, x_j)

For PF-NPSE, partition observations into groups of size at most m, compute k groups, and use the same formula with k replacing n and group score predictions replacing single-observation scores.

Validation

Run:

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

The tests verify the paper formulas, grouping behavior, and invariance to group order for deterministic score terms.

Limitations

This skill does not decide whether score estimates are accurate. It only enforces the algebraic composition contract from the paper.