Boltzmann MapReduce: A Partition-Function Reduce for Forkable Sandboxes
This paper proposes interpreting the MapReduce reduce operation as a partition function in statistical mechanics. Under local asymptotic normality (LAN), the confidence density emitted by a worker is a Gibbs–Boltzmann measure with inverse temperature equal to sample size. This leads to precision-weighted pooling and frequentist consistency as the zero-temperature limit.
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[Submitted on 17 Jun 2026]
Title:Boltzmann MapReduce: A Partition-Function Reduce for Forkable Sandboxes
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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: N/A
Subjects:
Artificial Intelligence (cs.AI); Probability (math.PR); Statistics Theory (math.ST)
MSC classes: N/A
Cite as: arXiv:2607.09689 [cs.AI]
(or arXiv:2607.09689v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2607.09689
arXiv-issued DOI via DataCite
Submission history
From: Yossi Eliaz [view email] [v1] Wed, 17 Jun 2026 16:26:18 UTC (538 KB)
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