← 研踪 PaperTrailarXiv:2611.16315 · v1
Shared Item-Level Error Limits the Aggregation of Small Language Models in Fermi Estimation
首次提交 2026-11-12 13:23
版本更新 2026-11-12 13:23
雷达观测 2026-11-13 14:16
摘要
Multi-agent systems of language models are often motivated by an averaging argument: if the agents' errors are unbiased and independent, the error of an aggregate of N answers falls as 1/sqrt(N). Fermi estimation, whose continuous answers are aggregated on the logarithmic scale, permits a direct test. We decompose the log10 error of each answer into the mean error of its model on the item, common to all its draws on the item, and a residual, and estimate both from 2.51M answers given before any communication by 15 open-weight models (3B-72B) on realFP, with replication under a single prompt pair on realFP, Science Olympiad Fermi questions and a guesstimation set. Given the item, teammates' errors are uncorrelated and teams behave as independent draws, but the item-level component accounts for a median 0.906 of the error variance over items. Teams of thirty therefore reduce a single agent's error by a median 1.7% (at most 5.4%), whereas draws that were also unbiased on each item would reduce it by 74-79%. All models compress their estimates toward about 10^6; this trend explains a median 17% of the item-level component, and a cross-validated linear recalibration on labelled items removes the overall bias but not that component. Three rounds of debate reduce within-team dispersion by 93% and leave the item-level component unchanged; revision without peers attains the same small gain. Mixing five models of similar accuracy reduces error by 6.6% relative to their own homogeneous teams, but no mixture improves on the most accurate model. Higher sampling temperature changes team error by about 1% at most, and contrastive activation steering not detectably; per-agent scaffold prompts (not significant after multiplicity correction) and skipping one layer in a single-model screen improve it. The results are conditional on the models, benchmarks, prompts and settings tested.
作者备注：21 pages, 2 figures, 17 tables
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v1 · 2026-11-12 13:23 · 最新观测版本
Shared Item-Level Error Limits the Aggregation of Small Language Models in Fermi Estimation
Multi-agent systems of language models are often motivated by an averaging argument: if the agents' errors are unbiased and independent, the error of an aggregate of N answers falls as 1/sqrt(N). Fermi estimation, whose continuous answers are aggregated on the logarithmic scale, permits a direct test. We decompose the log10 error of each answer into the mean error of its model on the item, common to all its draws on the item, and a residual, and estimate both from 2.51M answers given before any communication by 15 open-weight models (3B-72B) on realFP, with replication under a single prompt pair on realFP, Science Olympiad Fermi questions and a guesstimation set. Given the item, teammates' errors are uncorrelated and teams behave as independent draws, but the item-level component accounts for a median 0.906 of the error variance over items. Teams of thirty therefore reduce a single agent's error by a median 1.7% (at most 5.4%), whereas draws that were also unbiased on each item would reduce it by 74-79%. All models compress their estimates toward about 10^6; this trend explains a median 17% of the item-level component, and a cross-validated linear recalibration on labelled items removes the overall bias but not that component. Three rounds of debate reduce within-team dispersion by 93% and leave the item-level component unchanged; revision without peers attains the same small gain. Mixing five models of similar accuracy reduces error by 6.6% relative to their own homogeneous teams, but no mixture improves on the most accurate model. Higher sampling temperature changes team error by about 1% at most, and contrastive activation steering not detectably; per-agent scaffold prompts (not significant after multiplicity correction) and skipping one layer in a single-model screen improve it. The results are conditional on the models, benchmarks, prompts and settings tested.
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