# MUX: Continuous Reasoning via Multiplexed Tokens

arXiv: https://arxiv.org/abs/2607.18264 · HTML: https://mlsanity.com/paper/2607.18264/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 22 of its 63 references that are in the map.
- First posted on arXiv 19 May 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, 22 of 22)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://mlsanity.com/paper/2405.14838/) (2024)
- [Compressed Chain of Thought: Efficient Reasoning Through Dense Representations](https://mlsanity.com/paper/2412.13171/) (2024)
- [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://mlsanity.com/paper/2311.01460/) (2023)
- [SoftCoT++: Test-Time Scaling with Soft Chain-of-Thought Reasoning](https://mlsanity.com/paper/2505.11484/) (2025)
- [LLM Latent Reasoning as Chain of Superposition](https://mlsanity.com/paper/2510.15522/) (2025)
- [Thinking Tokens for Language Modeling](https://mlsanity.com/paper/2405.08644/) (2024)
- [Do Latent Tokens Think? A Causal and Adversarial Analysis of Chain-of-Continuous-Thought](https://mlsanity.com/paper/2512.21711/) (2025)
- [SofT-GRPO: Surpassing Discrete-Token LLM Reinforcement Learning via Gumbel-Reparameterized Soft-Thinking Policy Optimization](https://mlsanity.com/paper/2511.06411/) (2025)
- [Towards eliciting latent knowledge from LLMs with mechanistic interpretability](https://mlsanity.com/paper/2505.14352/) (2025)
- [Multiplex Thinking: Reasoning via Token-wise Branch-and-Merge](https://mlsanity.com/paper/2601.08808/) (2026)
- [Do Latent-CoT Models Think Step-by-Step? A Mechanistic Study on Sequential Reasoning Tasks](https://mlsanity.com/paper/2602.00449/) (2026)
- [How Do Latent Reasoning Methods Perform Under Weak and Strong Supervision?](https://mlsanity.com/paper/2602.22441/) (2026)
- [Are Latent Reasoning Models Easily Interpretable?](https://mlsanity.com/paper/2604.04902/) (2026)
- [Chain Of Thought Compression: A Theoretical Analysis](https://mlsanity.com/paper/2601.21576/) (2026)

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

- [Thinking with Looped Flows](https://mlsanity.com/paper/2609.11801/) (2026)
- [INTACT: Inducing Latent Reasoning on a Frozen Backbone](https://mlsanity.com/paper/2610.19568/) (2026)

## Abstract (arXiv)

Language models solve complex problems by articulating intermediate reasoning steps in natural language. While effective, this process is computationally bottlenecked: each reasoning step conveys only a single subword, and many are spent expressing a thought instead of carrying out computation. We propose MUX, a simple method for high-bandwidth and compact reasoning based on distillation of discrete reasoning into continuous multiplexed tokens in a latent space. Here, each latent token is trained to represent a weighted linear superposition (multiplexing) of a span of discrete reasoning subwords, where this superposition is lossless by construction and the span can be fully recovered (demultiplexing). We prove that simple position-dependent weightings, such as suitable geometric decay, support lossless multiplexing, which in turn prevents shortcut behaviors caused by latent collapse. We further show that multiplexed reasoning can perform parallel exploration in problems that require search. Across 32 evaluation settings spanning four language models, MUX outperforms strong latent reasoning baselines. Ablation and probing analyses further show that the learned latent tokens encode faithful and interpretable reasoning. Our results suggest that lossless superposition as local learning targets constitutes a sufficient condition for achieving strong and efficient latent continuous reasoning.