@inproceedings{firke-kannan-2026-reasoning,
title = "When Does Reasoning Age? Survival Analysis of Step-Level Error Hazard in {LLM} Chains",
author = "Firke, Raj and
Kannan, Rajeswari",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.1976/",
pages = "44972--44988",
ISBN = "979-8-89176-459-0",
abstract = "We apply survival analysis to study how the probability of reasoning error evolves across steps in LLM chain-of-thought inference. Analyzing 18,969 chains across five benchmarks and seven models (3B{--}70B) under greedy decoding, we discover a near-universal aging effect{---}the conditional probability of reasoning error increasing with step depth{---}as measured by the Weibull shape parameter $\rho > 1$ (indicating increasing hazard) in 34 of 35 dataset{--}model cells (binomial $p = 10^{-9}$), with task-dependent magnitude ranging from $\bar{\rho} = 1.35$ (multi-domain QA) to $\bar{\rho} = 2.36$ (logical deduction). This finding is robust to informative censoring (IPCW adjustment: 34/35 cells retain $\rho > 1$) and unobserved problem-level heterogeneity (shared frailty $\theta \approx 0$: 34/35 cells retain $\rho > 1$). Compositional fan-in{---}the number of prior-step outputs consumed per step{---}shows a large but statistically suggestive rank correlation with aging magnitude (Spearman $\rho_s = 0.90$, exact permutation $p = 0.083$, $N = 5$). We show that a survivorship bias masks these dynamics when raw error rates are used instead of the conditional hazard function. Held-out verification experiments confirm that late-weighted allocation (motivated by the aging finding) catches 94{\%} of errors vs. 23{\%} uniform on the strongest-aging task at budget $K{=}1$, while hazard-proportional allocation outperforms both baselines on moderately aging tasks (GSM8K, MathQA) at all budget levels. Our framework requires no training and provides actionable diagnostics for verification allocation."
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<abstract>We apply survival analysis to study how the probability of reasoning error evolves across steps in LLM chain-of-thought inference. Analyzing 18,969 chains across five benchmarks and seven models (3B–70B) under greedy decoding, we discover a near-universal aging effect—the conditional probability of reasoning error increasing with step depth—as measured by the Weibull shape parameter ρ > 1 (indicating increasing hazard) in 34 of 35 dataset–model cells (binomial p = 10⁻9), with task-dependent magnitude ranging from \barρ = 1.35 (multi-domain QA) to \barρ = 2.36 (logical deduction). This finding is robust to informative censoring (IPCW adjustment: 34/35 cells retain ρ > 1) and unobserved problem-level heterogeneity (shared frailty θ \approx 0: 34/35 cells retain ρ > 1). Compositional fan-in—the number of prior-step outputs consumed per step—shows a large but statistically suggestive rank correlation with aging magnitude (Spearman ρ_s = 0.90, exact permutation p = 0.083, N = 5). We show that a survivorship bias masks these dynamics when raw error rates are used instead of the conditional hazard function. Held-out verification experiments confirm that late-weighted allocation (motivated by the aging finding) catches 94% of errors vs. 23% uniform on the strongest-aging task at budget K=1, while hazard-proportional allocation outperforms both baselines on moderately aging tasks (GSM8K, MathQA) at all budget levels. Our framework requires no training and provides actionable diagnostics for verification allocation.</abstract>
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%0 Conference Proceedings
%T When Does Reasoning Age? Survival Analysis of Step-Level Error Hazard in LLM Chains
%A Firke, Raj
%A Kannan, Rajeswari
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F firke-kannan-2026-reasoning
%X We apply survival analysis to study how the probability of reasoning error evolves across steps in LLM chain-of-thought inference. Analyzing 18,969 chains across five benchmarks and seven models (3B–70B) under greedy decoding, we discover a near-universal aging effect—the conditional probability of reasoning error increasing with step depth—as measured by the Weibull shape parameter ρ > 1 (indicating increasing hazard) in 34 of 35 dataset–model cells (binomial p = 10⁻9), with task-dependent magnitude ranging from \barρ = 1.35 (multi-domain QA) to \barρ = 2.36 (logical deduction). This finding is robust to informative censoring (IPCW adjustment: 34/35 cells retain ρ > 1) and unobserved problem-level heterogeneity (shared frailty θ \approx 0: 34/35 cells retain ρ > 1). Compositional fan-in—the number of prior-step outputs consumed per step—shows a large but statistically suggestive rank correlation with aging magnitude (Spearman ρ_s = 0.90, exact permutation p = 0.083, N = 5). We show that a survivorship bias masks these dynamics when raw error rates are used instead of the conditional hazard function. Held-out verification experiments confirm that late-weighted allocation (motivated by the aging finding) catches 94% of errors vs. 23% uniform on the strongest-aging task at budget K=1, while hazard-proportional allocation outperforms both baselines on moderately aging tasks (GSM8K, MathQA) at all budget levels. Our framework requires no training and provides actionable diagnostics for verification allocation.
%U https://aclanthology.org/2026.emnlp-main.1976/
%P 44972-44988
Markdown (Informal)
[When Does Reasoning Age? Survival Analysis of Step-Level Error Hazard in LLM Chains](https://aclanthology.org/2026.emnlp-main.1976/) (Firke & Kannan, EMNLP 2026)
ACL