[2607.09689] Boltzmann MapReduce: A Partition-Function Reduce for Forkable Sandboxes

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Computer Science > Artificial Intelligence

arXiv:2607.09689 (cs)

[Submitted on 17 Jun 2026]

Title:Boltzmann MapReduce: A Partition-Function Reduce for Forkable Sandboxes

Authors:Yossi Eliaz<br>View a PDF of the paper titled Boltzmann MapReduce: A Partition-Function Reduce for Forkable Sandboxes, by Yossi Eliaz

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Abstract:To leading order under local asymptotic normality (LAN), the confidence density a worker emits over a chunk of size $n$ is a Gibbs--Boltzmann measure $\exp\{-\beta E(\theta)\}$ whose inverse temperature is the sample size, $\beta=n$. Three consequences are exact in the Gaussian/linear case and first-order otherwise: disjoint chunks carry independent Boltzmann factors, so the MapReduce \emph{reduce}, read literally, is a partition function $Z=\int\prod_k h_k\,d\theta$ whose mode is precision-weighted (inverse-variance) pooling; frequentist consistency is the zero-temperature limit $T=1/n\to0$

Comments:<br>N/A

Subjects:

Artificial Intelligence (cs.AI); Probability (math.PR); Statistics Theory (math.ST)

MSC classes:<br>N/A

Cite as:<br>arXiv:2607.09689 [cs.AI]

(or<br>arXiv:2607.09689v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2607.09689

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arXiv-issued DOI via DataCite

Submission history<br>From: Yossi Eliaz [view email]<br>[v1]<br>Wed, 17 Jun 2026 16:26:18 UTC (538 KB)

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