Boltzmann MapReduce: A Partition-Function Reduce for Forkable Sandboxes
Quick Answer
The paper introduces Boltzmann MapReduce, a method leveraging Gibbs-Boltzmann measures for efficient data processing in MapReduce frameworks.
Quick Take
It demonstrates that disjoint data chunks yield independent Boltzmann factors, allowing for precision-weighted pooling and frequentist consistency as sample sizes increase. This approach enhances the theoretical foundation of partition functions in statistical learning.
Key Points
- Boltzmann MapReduce applies Gibbs-Boltzmann measures for data chunk processing.
- Independent Boltzmann factors arise from disjoint data chunks in the framework.
- Precision-weighted pooling is achieved through partition function integration.
- Frequentist consistency is observed in the zero-temperature limit.
- The method enhances theoretical understanding of statistical learning processes.
Paper Resources
📖 Reader Mode
~1 min readAbstract: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)
— Originally published at arxiv.org
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