# Learning to Reason via Mixture-of-Thought for Logical Reasoning

arXiv: https://arxiv.org/abs/2505.15817 · HTML: https://mlsanity.com/paper/2505.15817/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 36 of its 43 references that are in the map.
- First posted on arXiv 21 May 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 36)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Self-Taught Optimizer (STOP): Recursively Self-Improving Code Generation](https://mlsanity.com/paper/2310.02304/) (2023)
- [Large Language Model Cascades with Mixture of Thoughts Representations for Cost-efficient Reasoning](https://mlsanity.com/paper/2310.03094/) (2023)
- [Faithful Logical Reasoning via Symbolic Chain-of-Thought](https://mlsanity.com/paper/2405.18357/) (2024)
- [Self-Taught Evaluators](https://mlsanity.com/paper/2408.02666/) (2024)
- [Self-Contrast: Better Reflection Through Inconsistent Solving Perspectives](https://mlsanity.com/paper/2401.02009/) (2024)
- [Lean-STaR: Learning to Interleave Thinking and Proving](https://mlsanity.com/paper/2407.10040/) (2024)
- [START: Self-taught Reasoner with Tools](https://mlsanity.com/paper/2503.04625/) (2025)
- [Exploring Human-Like Translation Strategy with Large Language Models](https://mlsanity.com/paper/2305.04118/) (2023)
- [Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective](https://mlsanity.com/paper/2501.11110/) (2025)
- [Large Language Models Meet Symbolic Provers for Logical Reasoning Evaluation](https://mlsanity.com/paper/2502.06563/) (2025)
- [Divide and Translate: Compositional First-Order Logic Translation and Verification for Complex Logical Reasoning](https://mlsanity.com/paper/2410.08047/) (2024)
- [Logic-of-Thought: Injecting Logic into Contexts for Full Reasoning in Large Language Models](https://mlsanity.com/paper/2409.17539/) (2024)

## Built on by (most cited first, 20 of 20)

- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [Self-Rewarding Vision-Language Model via Reasoning Decomposition](https://mlsanity.com/paper/2508.19652/) (2025)
- [Parallel-R1: Towards Parallel Thinking via Reinforcement Learning](https://mlsanity.com/paper/2509.07980/) (2025)
- [One Token to Fool LLM-as-a-Judge](https://mlsanity.com/paper/2507.08794/) (2025)
- [Evolving Language Models without Labels: Majority Drives Selection, Novelty Promotes Variation](https://mlsanity.com/paper/2509.15194/) (2025)
- [Emergent Hierarchical Reasoning in LLMs through Reinforcement Learning](https://mlsanity.com/paper/2509.03646/) (2025)
- [CDE: Curiosity-Driven Exploration for Efficient Reinforcement Learning in Large Language Models](https://mlsanity.com/paper/2509.09675/) (2025)
- [Dissecting Logical Reasoning in LLMs: A Fine-Grained Evaluation and Supervision Study](https://mlsanity.com/paper/2506.04810/) (2025)
- [ImAgent: A Unified Multimodal Agent Framework for Test-Time Scalable Image Generation](https://mlsanity.com/paper/2511.11483/) (2025)
- [Multi-Crit: Benchmarking Multimodal Judges on Pluralistic Criteria-Following](https://mlsanity.com/paper/2511.21662/) (2025)
- [CoBA-RL: Capability-Oriented Budget Allocation for Reinforcement Learning in LLMs](https://mlsanity.com/paper/2602.03048/) (2026)
- [R1-RE: Cross-Domain Relation Extraction with RLVR](https://mlsanity.com/paper/2507.04642/) (2025)
- [ProtoReasoning: Prototypes as the Foundation for Generalizable Reasoning in LLMs](https://mlsanity.com/paper/2506.15211/) (2025)
- [Stable and Efficient Single-Rollout RL for Multimodal Reasoning](https://mlsanity.com/paper/2512.18215/) (2025)
- [Training Large Language Models To Reason In Parallel With Global Forking Tokens](https://mlsanity.com/paper/2510.05132/) (2025)
- [Putting on the Thinking Hats: A Survey on Chain of Thought Fine-tuning from the Perspective of Human Reasoning Mechanism](https://mlsanity.com/paper/2510.13170/) (2025)
- [Agentic-R1: Distilled Dual-Strategy Reasoning](https://mlsanity.com/paper/2507.05707/) (2025)
- [Prompting Test-Time Scaling Is A Strong LLM Reasoning Data Augmentation](https://mlsanity.com/paper/2510.09599/) (2025)
- [VeriTrans: Fine-Tuned LLM-Assisted NL-to-PL Translation via a Deterministic Neuro-Symbolic Pipeline](https://mlsanity.com/paper/2604.10341/) (2026)
- [Separate First, Fuse Later: Mitigating Cross-Modal Interference in Audio-Visual LLMs Reasoning with Modality-Specific Chain-of-Thought](https://mlsanity.com/paper/2605.09906/) (2026)

## Abstract (arXiv)

Human beings naturally utilize multiple reasoning modalities to learn and solve logical problems, i.e., different representational formats such as natural language, code, and symbolic logic. In contrast, most existing LLM-based approaches operate with a single reasoning modality during training, typically natural language. Although some methods explored modality selection or augmentation at inference time, the training process remains modality-blind, limiting synergy among modalities. To fill in this gap, we propose Mixture-of-Thought (MoT), a framework that enables LLMs to reason across three complementary modalities: natural language, code, and a newly introduced symbolic modality, truth-table, which systematically enumerates logical cases and partially mitigates key failure modes in natural language reasoning. MoT adopts a two-phase design: (1) self-evolving MoT training, which jointly learns from filtered, self-generated rationales across modalities; and (2) MoT inference, which fully leverages the synergy of three modalities to produce better predictions. Experiments on logical reasoning benchmarks including FOLIO and ProofWriter demonstrate that our MoT framework consistently and significantly outperforms strong LLM baselines with single-modality chain-of-thought approaches, achieving up to +11.7pp average accuracy gain. Further analyses show that our MoT framework benefits both training and inference stages; that it is particularly effective on harder logical reasoning problems; and that different modalities contribute complementary strengths, with truth-table reasoning helping to overcome key bottlenecks in natural language inference.