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name: factorized_score_composition description: Compose F-NPSE and PF-NPSE posterior scores from prior corrections and per-condition score estimates.

Factorized Score Composition

Use this skill when implementing or auditing the core F-NPSE/PF-NPSE inference-time score. It should be called before sampling so the recovery can prove that additive score composition, not duplicated harness logic, produced the score.

Inputs

• Current theta vector.
• A progress value (T - t) / T in [0, 1].
• Per-observation scores for F-NPSE, or per-subset scores for PF-NPSE.
• Prior score vector, typically -theta under standard-normal reparameterization.
• Condition count: number of observations for F-NPSE or number of subsets for PF-NPSE.

Outputs

• Composed score vector.
• Trace with score sum, prior correction, condition count, progress, and mode.

Workflow

1. Validate all score vectors have the same dimensionality.
2. Sum learned condition scores.
3. Compute the correction (1 - condition_count) * progress * prior_score.
4. Add the correction to the score sum.
5. Return a trace so downstream recovery can verify the sign and count semantics.

Validation

Run python tests/test_factorized_score_composition.py or the Distiller skill-tree validator.

Limitations

This skill composes supplied score estimates. It does not train the score network and does not sample posterior particles by itself.