{"ID":6579336,"CreatedAt":"2026-07-14T13:45:26.706163626Z","UpdatedAt":"2026-07-14T15:22:39.611211464Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.09689","arxiv_id":"2607.09689","title":"Boltzmann MapReduce: A Partition-Function Reduce for Forkable Sandboxes","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 $\\exp\\{-βE(θ)\\}$ whose inverse temperature is the sample size, $β=n$. 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 $Z=\\int\\prod_k h_k\\,dθ$ whose mode is precision-weighted (inverse-variance) pooling; frequentist consistency is the zero-temperature limit $T=1/n\\to0$","short_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 $\\exp\\{-βE(θ)\\}$ whose inverse temperature is the sample size, $β=n$. Three consequences are exact in the Gaussian/linear case and first-order otherwise: disjoint chunks...","url_abs":"https://arxiv.org/abs/2607.09689","url_pdf":"https://arxiv.org/pdf/2607.09689v1","authors":"[\"Yossi Eliaz\"]","published":"2026-06-17T16:26:18Z","proceeding":"cs.AI","tasks":"[\"cs.AI\",\"math.PR\",\"math.ST\"]","methods":"[]","has_code":false}