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name: binary_nce_estimator description: Compute binary conditional NCE objectives and diagnose self-normalization failures in finite protocols.

Binary NCE Estimator

Use this skill when a recovery needs the binary data-vs-noise objective from conditional NCE or needs to diagnose whether the binary objective is valid for a conditional model. The key check is whether the conditional partition function can be treated as constant in x or modeled explicitly.

Do not use this skill to claim full conditional-model consistency when Z(x) varies and no per-input normalizer is present.

Inputs

• A ConditionalNCEProtocol.
• A score function and scalar offset.
• K, inherited from the protocol.
• Optional parameters for the Section 4.3 paper counterexample.

Outputs

• Binary objective value.
• Data-vs-noise posterior g(x,y;theta,c).
• Self-normalization diagnostics.
• Analytic binary optimum ratio for the Section 4.3 counterexample.

Workflow

1. Compute bar_s=s-log p_N.
2. Compute:

g(x,y;theta,c) = exp(bar_s(x,y;theta)-c) /
                 (exp(bar_s(x,y;theta)-c) + K)

3. Accumulate data and noise log terms.
4. Check partition variation across inputs.
5. For the Section 4.3 counterexample, expose the paper's analytic binary limit theta1/theta2=3/7.

Validation

Run the Distiller validator with tests. The tests assert that the Section 4.3 true ratio is 1/3, the binary limit is 3/7, and the normalizers differ across inputs.

Limitations

The included optimizer and analytic diagnostic are for finite recovery and mechanism checks. They are not a replacement for full neural NCE training.