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玻尔兹曼MapReduce:可分叉沙盒的配分函数归约

Evidence-Aware MapReduce for Forkable Compute

Yossi Eliaz

arXiv 2607.09689首次发表:更新:

发表机构

Incredibuild; HIT CS Department(Incredibuild公司; 以色列理工学院计算机科学系)

机构由 AI 辅助整理,请以论文原文为准。

AI 中文总结

研究在局部渐近正态性下工作节点发出的置信密度,指出其为吉布斯 - 玻尔兹曼测度,逆温度是样本大小。高斯/线性下相关结果精确,MapReduce归约是配分函数,还有频率主义一致性等结论。

AI 中文摘要

在局部渐近正态性(LAN)下到主导阶,工作节点在大小为\(n\)的块上发出的置信密度是一个吉布斯 - 玻尔兹曼测度\(\exp\{-\beta E(\theta)\}\),其逆温度为样本大小\(\beta = n\)。在高斯/线性情况下这三个结果是精确的,否则是一阶的:不相交块携带独立的玻尔兹曼因子,所以MapReduce的归约实际上是一个配分函数\(Z=\int\prod_k h_k\,d\theta\),其模式是精度加权(逆方差)合并;频率主义一致性是零温度极限\(T = 1/n\to0\)。

英文摘要

Snapshot-backed sandboxes make branching cheap while leaving evidence dependence unchanged. Branches can reuse a model, prompt, repository, tests, observations, or execution ancestor, so counting outputs can amplify one repeated error into high-confidence consensus. We introduce an \emph{evidence-aware reduction contract}: each worker reports an estimate, estimated information, evidence identifiers, fork lineage, and execution metadata. For independent workers estimating one common parameter, we use standard inverse-information pooling in its Gaussian/Wald form. The fixed-dimensional numeric summary can merge in any tree order; evidence IDs and lineage follow separate rules. The residual $Δ$ measures disagreement, becomes Cochran's $Q$ in the scalar inverse-variance case, and appears in the product integral. A reference implementation validates serialized records, rejects repeated nonempty evidence identifiers, carries evidence and lineage through tree reduction, and uses Cholesky-based numerical linear algebra. Unit tests and seeded synthetic checks exercise the algebra, unequal information, and forged precision; one four-worker named-snapshot trace exercises the end-to-end path. Platform logs document the exercised execution paths. A central open systems challenge is to turn evidence identity and fork lineage into a dependence model for correlated and adaptively selected AI branches.

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