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name: importance_sampling_generation description: Estimate residual EBM partition terms and select text continuations by importance reweighting fixed-LM proposal samples.

Importance Sampling Generation

Use this skill when evaluating or generating from a residual text EBM with a fixed language-model proposal. It provides the paper's practical mechanism for avoiding MCMC over discrete text.

Do not use this skill to claim full perplexity from a tiny sample set. Small candidate sets are reduced/proxy evidence unless they match the paper's estimator scale and data protocol.

Inputs

• Candidate continuations sampled from the fixed base LM.
• Energy scores for each continuation.
• Optional base-LM log probabilities for residual joint ranking.
• Optional token count and target continuation for a reduced perplexity-style calculation.

Outputs

• log_z_estimate: sample estimate of log E_{P_LM}[exp(-E)].
• Normalized weights proportional to exp(-E).
• Selected continuation by energy-only importance weight for generation, with residual joint score retained as a diagnostic when base-LM log probabilities are available.
• Effective sample size and concentration diagnostics.

Workflow

1. Compute stable log mean exp(-energy) across proposal samples.
2. Normalize exp(-energy) into candidate weights.
3. Select the best deterministic candidate by normalized exp(-E) weight, using proposal log probability only as a tie-break when energy weights are exactly tied. Keep lm_logprob - energy as an evaluation/ranking diagnostic, not the default generation selector.
4. Report effective sample size so inefficient proposal search is visible.
5. Keep proposal provenance separate from residual-energy scoring.

Validation

Run:

python scripts/importance_sampling.py --demo
python -m pytest tests

The tests verify stable log-mean-exp behavior, normalized weights, increased weight for lower energy, and generation selection by energy weight even when a negative candidate has a high proposal log probability.

Limitations

Importance sampling quality depends on proposal coverage. A poor base LM can make residual search inefficient, exactly as the paper notes. Record sample count and proposal source in recovery artifacts.