What is verifier exploitability?

Sampling more candidates raises coverage, the chance that at least one is correct, but someone still has to pick the winner. Brown et al. showed coverage scaling with the number of samples over four orders of magnitude. Our verifier exploitability paper (now a superseded draft) splits verifier quality into discrimination d′ and exploitability ε. With ε = 0, an honest but noisy verifier, more sampling never hurts. Any ε > 0 makes accuracy non-monotone in N: it peaks at a computable budget N*(ε) and then declines. Better discrimination raises the peak but gives no immunity.

In the reference simulation of the successor paper, Thurstone bounds Best-of-N, coverage approaches 1 while accuracy peaks at 0.70 at N = 64 and falls to 0.36 by N = 8192.

Inverting the reward-model overoptimization curves published by Gao, Schulman and Hilton implies real verifiers sit around ε ≈ 0.002–0.05. Exploitability is also not a fixed property of the verifier: in a later note the same verifier measured 0.153 to 0.949, a 6.2× range, depending only on the prefilter that supplied its candidates. It belongs to the verifier–pool pair.

No. Our correction states that the pairwise form ε = Φ(−gap/(σ√2)) is Thurstone's Law of Comparative Judgment, Case V, from 1927: an identity, not a discovery, and not a universality class. Under heavy-tailed score noise it is off by 723×, so ε should be estimated directly. The measured constants, the consensus threshold ε* = p/(1−p) and the tools stand.

"Verifier exploitability" is NeuroGenesys's own term of art; we found no standard external definition. The closest established ideas are reward hacking, formalised by Skalse et al. as optimising an imperfect proxy until the true reward falls, and Goodhart effects in reward-model optimisation.

Counting rather than ranking. Plurality voting among high scorers defeats the collapse unless a shared exploit beats a plurality, with a threshold at ε* = p/(1−p). In When the exploit is constructed, Best-of-8192 accuracy was 0.862 with sampled exploits and 0.000 with exploits constructed against the checker, while plurality voting held at 0.999. That note also corrected the threshold for a regime where a single wrong answer dominates the vote.

• RelatedTest-time compute cost estimator (free tool)
• Topic hubTopic hub: test-time compute and verification
• RelatedThurstone bounds Best-of-N (paper)
• Relatedverifier-budget: compute N*(ε) in the browser
• RelatedLesson: when the verifier is the bottleneck