Agreeing on the Answer but Not the Reason: Measurement Limits of LLM Reasoning Failure Taxonomies
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Summary
arXiv:2611.13140v1 Announce Type: new Abstract: Failure taxonomies for LLM reasoning are increasingly reported as measurements: papers state what fraction of a model's errors fall into named categories, then compare those fractions across models. We show that for one such category the reported fraction is largely a property of the measurement procedure. We defined Compositional Collapse (a model notices a required sub-part of a problem, then drops or misapplies it) and measured it across twelve models and eleven languages on a public multilingual math benchmark (2,316 graded records). First, 50.1% of failures carry evidence for more than one category, so the reported plurality depends on the order in which the classifier tests them: reversing two tests moves it in eleven of twelve models, and across all six orderings Collapse's share spans 26.4% to 76.4%. Second, agreement collapses for the category but not for the task. Native speakers of all eleven languages judged 179 transcripts, agreeing with our inspector at kappa = 0.932 on answer correctness but only kappa = 0.093 on Collapse. A second native speaker per language re-rated 142 items; on 121 determinate pairs the two humans agree with each other at kappa = 0.659, while each agrees with the inspector at kappa <= 0.094. Re-running the same inspector model with the human instructions verbatim raises kappa against Human 2 from 0.147 to 0.636, so the gap is largely attributable to the prompt, not the model. Third, the inspector labels Collapse 1.81 times as often as native speakers, but only 1.17 times once a defective benchmark item (a deleted clause in the Bengali and Chinese translations) is excluded. We recommend four cheap checks before comparing failure-mode rates across models: report label co-occurrence, permute the tie-break, validate on a shared independent sample, and audit systematic disagreements.
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