aiqbench analysis
This preregistered reproduction validates the predictive power of chain-of-thought entropy trajectory shapes for model correctness while demonstrating that total entropy drop magnitude is highly context-dependent across benchmarks and model families. The findings clarify which reliability signals are robust under full-scale testing versus those requiring specific protocol conditions, offering critical insights for evaluating reasoning-distilled models.
Chain-of-Thought Entropy as a Reliability Signal: A Preregistered Reproduction
arXiv:2609.19606v1 Announce Type: new Abstract: This empirical study is an independent reproduction of the dissociation Zhao reported in 2026. The shape of a large language model's chain-of-thought entropy trajectory predicts whether the final answer is correct, while the magnitude of its total entropy drop does not. The dissociation merits reproduction because the magnitude half rests on a single 300-problem run with one model at one seed, while the shape half was reported at full scale on both benchmarks and on a second model family. Registered at OSF before any confirmatory run, the reproduction crosses the complete GSM8K and MATH-500 benchmark test sets with four open-weight models including one reasoning-distilled model of a kind the original did not test. The shape signal replicates. The magnitude signal divides by setting. On the anchor model the accuracy gap between monotone and non-monotone chains is +9.6 percentage points on GSM8K and +27.5 on MATH-500, while the rank correlation of the total entropy drop with correctness is -0.018 on GSM8K and +0.414 on MATH-500. On the reasoning-distilled model the binary form of the shape signal fires on about one chain in a hundred, too few to estimate the registered contrast, while the graded violation count remains predictive there. In an exploratory comparison the final-step entropy alone outperforms the binary shape flag in all eight model-by-benchmark cells by ROC area, and in six or seven by the risk-coverage area the original reports, depending on an integration range the original does not state. The study contributes a reproduction of the shape signal at full test-set scale under seven documented protocol differences, a map of the settings where the magnitude signal holds and fails, and measurements of four protocol dependencies the original does not report.
Abstract:This empirical study is an independent reproduction of the dissociation Zhao reported in 2026. The shape of a large language model's chain-of-thought entropy trajectory predicts whether the final answer is correct, while the magnitude of its total entropy drop does not. The dissociation merits reproduction because the magnitude half rests on a single 300-problem run with one model at one seed, while the shape half was reported at full scale on both benchmarks and on a second model family. Registered at OSF before any confirmatory run, the reproduction crosses the complete GSM8K and MATH-500 benchmark test sets with four open-weight models including one reasoning-distilled model of a kind the original did not test. The shape signal replicates. The magnitude signal divides by setting. On the anchor model the accuracy gap between monotone and non-monotone chains is +9.6 percentage points on GSM8K and +27.5 on MATH-500, while the rank correlation of the total entropy drop with correctness is -0.018 on GSM8K and +0.414 on MATH-500. On the reasoning-distilled model the binary form of the shape signal fires on about one chain in a hundred, too few to estimate the registered contrast, while the graded violation count remains predictive there. In an exploratory comparison the final-step entropy alone outperforms the binary shape flag in all eight model-by-benchmark cells by ROC area, and in six or seven by the risk-coverage area the original reports, depending on an integration range the original does not state. The study contributes a reproduction of the shape signal at full test-set scale under seven documented protocol differences, a map of the settings where the magnitude signal holds and fails, and measurements of four protocol dependencies the original does not report.
Computation and Language (cs.CL); Machine Learning (cs.LG)
arXiv:2609.19606 [cs.CL]
(or arXiv:2609.19606v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2609.19606 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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