# Diversity Combining for Multi-Path LLM Reasoning

arXiv: https://arxiv.org/abs/2609.38829 · HTML: https://mlsanity.com/paper/2609.38829/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 28 of its 75 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 28 of 28)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [CRUXEval: A Benchmark for Code Reasoning, Understanding and Execution](https://mlsanity.com/paper/2401.03065/) (2024)
- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [Soft Thinking: Unlocking the Reasoning Potential of LLMs in Continuous Concept Space](https://mlsanity.com/paper/2505.15778/) (2025)
- [SoftCoT: Soft Chain-of-Thought for Efficient Reasoning with LLMs](https://mlsanity.com/paper/2502.12134/) (2025)
- [Let's Sample Step by Step: Adaptive-Consistency for Efficient Reasoning and Coding with LLMs](https://mlsanity.com/paper/2305.11860/) (2023)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [Escape Sky-high Cost: Early-stopping Self-Consistency for Multi-step Reasoning](https://mlsanity.com/paper/2401.10480/) (2024)
- [Reasoning Aware Self-Consistency: Leveraging Reasoning Paths for Efficient LLM Sampling](https://mlsanity.com/paper/2408.17017/) (2024)
- [BudgetThinker: Empowering Budget-aware LLM Reasoning with Control Tokens](https://mlsanity.com/paper/2508.17196/) (2025)
- [Joint Training of Deep Ensembles Fails Due to Learner Collusion](https://mlsanity.com/paper/2301.11323/) (2023)
- [Native Parallel Reasoner: Reasoning in Parallelism via Self-Distilled Reinforcement Learning](https://mlsanity.com/paper/2512.07461/) (2025)
- [The Sequential Edge: Inverse-Entropy Voting Beats Parallel Self-Consistency at Matched Compute](https://mlsanity.com/paper/2511.02309/) (2025)
- [Training Large Language Models To Reason In Parallel With Global Forking Tokens](https://mlsanity.com/paper/2510.05132/) (2025)
- [Optimal Aggregation of LLM and PRM Signals for Efficient Test-Time Scaling](https://mlsanity.com/paper/2510.13918/) (2025)

## Abstract (arXiv)

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.