Correlated verifier cascades can make LLM reliability plateau below 100%

Jiangang Han · hf · 2026-07-21

Partially correlated verifier cascades can hit reliability ceilings

This note studies serial verification gates in LLM harnesses, where an answer is returned only if all k verifier calls accept it.

Main results:

• Under latent correlation between verifier outcomes, the exact posterior becomes ellk = ell0 - ln mk, where mk is the k-th moment of a latent false-accept rate.
• The log-odds curve is concave in k, so the independence-based Odds Law is only a tangent/upper bound, not the general case.
• For Beta latent variables, failure decays polynomially rather than exponentially.
• If some errors are effectively blind spots, reliability can saturate below 1 no matter how many gates are added.
• When true-accept rates also vary, the system can eventually improve, plateau, or even get worse depending on tail behavior.

The practical takeaway is that decorrelation — changing model family, modality, or evidence source — matters more than simply adding more gates.

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