# Multiplex Thinking: Reasoning via Token-wise Branch-and-Merge

arXiv: https://arxiv.org/abs/2601.08808 · HTML: https://mlsanity.com/paper/2601.08808/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 30 references that are in the map.
- First posted on arXiv 13 Jan 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 20 of 20)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [Do Large Language Models Latently Perform Multi-Hop Reasoning?](https://mlsanity.com/paper/2402.16837/) (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)
- [Hopping Too Late: Exploring the Limitations of Large Language Models on Multi-Hop Queries](https://mlsanity.com/paper/2406.12775/) (2024)
- [Reasoning by Superposition: A Theoretical Perspective on Chain of Continuous Thought](https://mlsanity.com/paper/2505.12514/) (2025)
- [Learning Adaptive Parallel Reasoning with Language Models](https://mlsanity.com/paper/2504.15466/) (2025)
- [LLMs are Single-threaded Reasoners: Demystifying the Working Mechanism of Soft Thinking](https://mlsanity.com/paper/2508.03440/) (2025)
- [Soft Tokens, Hard Truths](https://mlsanity.com/paper/2509.19170/) (2025)
- [ThreadWeaver: Adaptive Threading for Efficient Parallel Reasoning in Language Models](https://mlsanity.com/paper/2512.07843/) (2025)

## Built on by (most cited first, 16 of 16)

- [Latent-GRPO: Group Relative Policy Optimization for Latent Reasoning](https://mlsanity.com/paper/2604.27998/) (2026)
- [LaDi-RL: Latent Diffusion Reasoning Prevents Entropy Collapse in Reinforcement Learning](https://mlsanity.com/paper/2602.01705/) (2026)
- [T^2MLR: Transformer with Temporal Middle-Layer Recurrence](https://mlsanity.com/paper/2607.15178/) (2026)
- [Latent Reasoning with Normalizing Flows](https://mlsanity.com/paper/2606.06447/) (2026)
- [Select to Think: Unlocking SLM Potential with Local Sufficiency](https://mlsanity.com/paper/2604.26940/) (2026)
- [Pair-In, Pair-Out: Latent Multi-Token Prediction for Efficient LLMs](https://mlsanity.com/paper/2605.27255/) (2026)
- [Efficient and Trainable Language Model Test-Time Scaling via Local Branch Routing](https://mlsanity.com/paper/2606.25354/) (2026)
- [Training Continuous Chain of Thought Models: A Tale of Two Regimes](https://mlsanity.com/paper/2607.16972/) (2026)
- [MUX: Continuous Reasoning via Multiplexed Tokens](https://mlsanity.com/paper/2607.18264/) (2026)
- [Break the Block: Dynamic-size Reasoning Blocks for Diffusion Large Language Models via Monotonic Entropy Descent with Reinforcement Learning](https://mlsanity.com/paper/2605.02263/) (2026)
- [Latent Thought Credit: Multi-Answer Credit Assignment for Latent Reasoning](https://mlsanity.com/paper/2608.01593/) (2026)
- [Block-R1: Rethinking the Role of Block Size in Multi-domain Reinforcement Learning for Diffusion Large Language Models](https://mlsanity.com/paper/2605.11726/) (2026)
- [CurveRL: Principled Distribution-Aware Context Reweighting for LLM Reasoning](https://mlsanity.com/paper/2605.24331/) (2026)
- [TARPO: Token-Wise Latent-Explicit Reasoning via Action-Routing Policy Optimization](https://mlsanity.com/paper/2606.05859/) (2026)
- [SuperThoughts: Reasoning Tokens in Superposition](https://mlsanity.com/paper/2606.13862/) (2026)
- [ANI: Adaptive Numerical Injection for Unifying Semantic and Arithmetic Representations in Numerical Reasoning](https://mlsanity.com/paper/2609.39294/) (2026)

## Abstract (arXiv)

Large language models often solve complex reasoning tasks more effectively with Chain-of-Thought (CoT), but at the cost of long, low-bandwidth token sequences. Humans, by contrast, often reason softly by maintaining a distribution over plausible next steps. Motivated by this, we propose Multiplex Thinking, a stochastic soft reasoning mechanism that, at each thinking step, samples K candidate tokens and aggregates their embeddings into a single continuous multiplex token. This preserves the vocabulary embedding prior and the sampling dynamics of standard discrete generation, while inducing a tractable probability distribution over multiplex rollouts. Consequently, multiplex trajectories can be directly optimized with on-policy reinforcement learning (RL). Importantly, Multiplex Thinking is self-adaptive: when the model is confident, the multiplex token is nearly discrete and behaves like standard CoT; when it is uncertain, it compactly represents multiple plausible next steps without increasing sequence length. Across challenging math reasoning benchmarks, Multiplex Thinking consistently outperforms strong discrete CoT and RL baselines from Pass@1 through Pass@1024, while producing shorter sequences. The code and checkpoints are available at https://github.com/GMLR-Penn/Multiplex-Thinking.