# Weaker LLMs' Opinions Also Matter: Mixture of Opinions Enhances LLM's Mathematical Reasoning

arXiv: https://arxiv.org/abs/2502.19622 · HTML: https://mlsanity.com/paper/2502.19622/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 26 Feb 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 27 of 27)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [Large Language Model based Multi-Agents: A Survey of Progress and Challenges](https://mlsanity.com/paper/2402.01680/) (2024)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [LLM-Blender: Ensembling Large Language Models with Pairwise Ranking and Generative Fusion](https://mlsanity.com/paper/2306.02561/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [TravelPlanner: A Benchmark for Real-World Planning with Language Agents](https://mlsanity.com/paper/2402.01622/) (2024)
- [Rethinking the Bounds of LLM Reasoning: Are Multi-Agent Discussions the Key?](https://mlsanity.com/paper/2402.18272/) (2024)
- [ProSA: Assessing and Understanding the Prompt Sensitivity of LLMs](https://mlsanity.com/paper/2410.12405/) (2024)
- [Teaching Arithmetic to Small Transformers](https://mlsanity.com/paper/2307.03381/) (2023)
- [Chain of Thoughtlessness? An Analysis of CoT in Planning](https://mlsanity.com/paper/2405.04776/) (2024)
- [LLMs Still Can't Plan; Can LRMs? A Preliminary Evaluation of OpenAI's o1 on PlanBench](https://mlsanity.com/paper/2409.13373/) (2024)
- [AgentLite: A Lightweight Library for Building and Advancing Task-Oriented LLM Agent System](https://mlsanity.com/paper/2402.15538/) (2024)
- [Beyond Chain-of-Thought, Effective Graph-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2305.16582/) (2023)
- [How Susceptible are LLMs to Influence in Prompts?](https://mlsanity.com/paper/2408.11865/) (2024)
- [Can We Rely on LLM Agents to Draft Long-Horizon Plans? Let's Take TravelPlanner as an Example](https://mlsanity.com/paper/2408.06318/) (2024)
- [Revealing the Barriers of Language Agents in Planning](https://mlsanity.com/paper/2410.12409/) (2024)
- [Think Outside the Code: Brainstorming Boosts Large Language Models in Code Generation](https://mlsanity.com/paper/2305.10679/) (2023)
- [On The Planning Abilities of OpenAI's o1 Models: Feasibility, Optimality, and Generalizability](https://mlsanity.com/paper/2409.19924/) (2024)

## Built on by (most cited first, 2 of 2)

- [Belief-Calibrated Multi-Agent Consensus Seeking for Complex NLP Tasks](https://mlsanity.com/paper/2510.06307/) (2025)
- [Reflective Confidence: Correcting Reasoning Flaws via Online Self-Correction](https://mlsanity.com/paper/2512.18605/) (2025)

## Abstract (arXiv)

Recent advances in Large Language Models (LLMs) have raised interest in their formal reasoning capabilities, particularly in mathematics. While closed LLMs like GPT-4 perform well on mathematical benchmarks, e.g., GSM8K, it remains unclear whether small to medium-sized open LLMs can achieve similar performance, questioning their reliability. To close this gap, we propose a post-training approach leveraging a mixture of opinions (MoO) from weaker ancillary LLMs to enhance a (relatively) stronger LLM's reasoning. For that, each post-training sample is augmented with Chain-of-Thought (CoT) reasoning steps and answers from ancillary LLMs, enabling the main LLM to learn from diverse perspectives. We compare MoO with standard supervised fine-tuning (SFT), few-shot prompting, and the Mixture of Agents (MoA) method on mathematical reasoning benchmarks. Our results show that incorporating weaker LLMs' opinions improves mathematical reasoning by an average of 5%, highlighting the value of diverse perspectives in reasoning tasks.