Diversity Combining for Multi-Path LLM Reasoning

A new arXiv paper (2609.38829v1) formalizes multi-path LLM reasoning as a diversity combining problem from wireless communications, showing that pairwise correlation of path correctness caps the effective sample size of self-consistency voting at a finite ceiling. Across 5 models and 12 benchmarks, prompt-template diversity reduced path correlation in 55 of 57 valid cells, with the strongest effect on open-ended QA, and an Adaptive-K rule using a four-path pilot to select K* retained 96–103% of MV@K=32 accuracy across Math, QA, and NLU.

arXiv:2609.38829v1 Announce Type: new Abstract: Multi-path reasoning methods such as self-consistency SC sample $K$ reasoning paths and choose the most frequent answer. However, their gains quickly plateau as $K$ increases, and existing methods do not predict when this saturation will occur. We formalize multi-path LLM reasoning as a diversity combining problem from wireless communications: each path is a noisy channel observation, and the pairwise correlation of path correctness caps the design-effect effective sample size of the vote at a finite ceiling. Generalized least squares GLS analysis shows that, under exchangeability, the optimal symmetric linear combiner of latent embeddings is uniform, supporting majority vote as the natural default in standard SC while leaving room for weighting or pruning under heterogeneous prompt-template branches. Across 5 models and 12 benchmarks, prompt-template diversity reduces path correlation in $55$ of $57$ valid cells, with the strongest effect on open-ended QA. We derive an Adaptive-K rule that uses a four-path pilot to select $K^ $, retaining $96$--$103\%$ of MV@$K{=}32$ accuracy across Math, QA, and NLU.