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Restricting chain-of-thought faithfulness scoring to correctly answered instances produced a 7.4 point selection gap on GLM-5.3, and 42.8 percent of that gap came from how many operations the task needed

AspireAI community · arXiv (cs.CL)
A common protocol in chain-of-thought faithfulness evaluation scores only the instances a model got right, which quietly changes the population being measured. This paper works out that selection step in a seven-variable structural causal model, deriving the exact observed gap as the covariance of the faithfulness and correctness variables divided by the correctness rate, and distinguishes difficulty confounding from shortcut-induced collider bias. Across four sub-ceiling arithmetic deployments it observes positive selection gaps in all four, with the primary GLM-5.3 run giving a +7.4 percentage-point gap at n=1,000 and p<0.0001, and a pooled Cochran-Mantel-Haenszel analysis giving OR=1.70. An assumption-free decomposition attributes 42.8 percent of the GLM-5.3 gap to between-stratum variation in how many operations were needed, leaving most of it unattributed. The practical alternative is to evaluate all traces directly, which estimates population faithfulness without correctness filtering whenever counterfactual compliance is observable for every instance.
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