MUX: Continuous Reasoning via Multiplexed Tokens

• URL: http://arxiv.org/abs/2607.18264v1
• Date: Tue, 19 May 2026 10:30:32 GMT
• Title: MUX: Continuous Reasoning via Multiplexed Tokens
• Abstract summary: Language models solve complex problems by articulating intermediate reasoning steps in natural language.<n>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.
• Score: 17.62611996930725
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• From Reasoning Depth to Reasoning Breadth: Evaluating Multi-Point Associative Reasoning in Large Language Models [18.240441114446607]
  We introduce MPAR-Bench, a benchmark that isolates reasoning breadth through multi-point associative reasoning.<n>We construct 1,000 items using a multi-agent clue-generation pipeline, embedding-based diversity filtering, and human verification.<n>We evaluate models using accuracy, ANLS, embedding similarity, reasoning-trace verification, and four perturbations: clue masking, order shuffling, distractor injection, and multi-step clues.
  arXiv  Detail & Related papers  (2026-08-11T03:58:23Z)
• Why Struggle with Continuous Latents? Interpretable Discrete Latent Reasoning via Rendered Compression [42.15219720606396]
  Large language models achieve high reasoning performance via explicit chain-of-thought and reinforcement learning.<n>Latent reasoning reduces this cost by shifting computation into a latent space.<n>We propose textbfDiscrete Latent Reasoning(DLR), the first method that converts continuous latent states into explicit discrete tokens.
  arXiv  Detail & Related papers  (2026-06-29T02:34:52Z)
• Thinking Without Words: Efficient Latent Reasoning with Abstract Chain-of-Thought [13.72996269125319]
  Abstract-CoT achieves up to $11.6times$ fewer reasoning tokens while demonstrating comparable performance across mathematical reasoning, instruction-following, and multi-hop reasoning.<n>Our findings highlight the potential for post-training latent reasoning mechanisms that enable efficient inference through a learned abstract reasoning language.
  arXiv  Detail & Related papers  (2026-04-24T16:45:51Z)
• SPOT: Span-level Pause-of-Thought for Efficient and Interpretable Latent Reasoning in Large Language Models [15.95627037350657]
  Explicit Chain-of-Thought (CoT) computation incurs high inference cost due to internalize token-level traces.<n>We propose SPOT, a flexible framework that compresses explicit CoT into compact latent pause tokens without enforcing a fixed response template.<n>Experiments on reasoning benchmarks demonstrate that SPOT improves accuracy by 2.3 points on average while reducing generated tokens by 37.5%.
  arXiv  Detail & Related papers  (2026-03-06T12:34:27Z)
• Latent Chain-of-Thought as Planning: Decoupling Reasoning from Verbalization [9.193078163792427]
  Chain-of-Thought (CoT) empowers Large Language Models (LLMs) to tackle complex problems.<n>Recent latent reasoning approaches attempt to optimize efficiency by performing reasoning within continuous hidden states.<n>We introduce PLaT, a framework that reformulates latent reasoning as planning by fundamentally decouple reasoning from verbalization.
  arXiv  Detail & Related papers  (2026-01-29T07:38:18Z)
• Multiplex Thinking: Reasoning via Token-wise Branch-and-Merge [87.51901436392427]
  Large language models often solve complex reasoning tasks more effectively with Chain-of-Thought (CoT)<n>Humans, by contrast, often reason softly by maintaining a tractable probability distribution over plausible next steps.<n>We propose Multiplex Thinking, a soft reasoning mechanism that samples K candidate tokens and aggregates their embeddings into a single continuous multiplex token.<n>Multiplex Thinking is self-adaptive: when the model is confident, the multiplex token is nearly discrete and behaves like standard CoT.
  arXiv  Detail & Related papers  (2026-01-13T18:48:00Z)
• Latent Reasoning in LLMs as a Vocabulary-Space Superposition [80.01651003144282]
  Large language models (LLMs) demonstrate strong reasoning abilities with chain-of-thought prompting, but explicit reasoning introduces substantial computational overhead.<n>Recent work on latent reasoning reduces this cost by reasoning in latent space without explicit supervision, but performance drops significantly.<n>To address this, we restrict the latent space to the column space of the LLM vocabulary, treating latent reasoning as a superposition over vocabulary probabilities.<n>Once latent reasoning concludes, it collapses into an eigenstate of explicit reasoning to yield the final answer.<n>Latent-SFT sets a new state of the art on GSM8k, matching explicit
  arXiv  Detail & Related papers  (2025-10-17T10:51:20Z)
• PixelThink: Towards Efficient Chain-of-Pixel Reasoning [70.32510083790069]
  PixelThink is a simple yet effective scheme that integrates externally estimated task difficulty and internally measured model uncertainty.<n>It learns to compress reasoning length in accordance with scene complexity and predictive confidence.<n> Experimental results demonstrate that the proposed approach improves both reasoning efficiency and overall segmentation performance.
  arXiv  Detail & Related papers  (2025-05-29T17:55:49Z)
• Soft Thinking: Unlocking the Reasoning Potential of LLMs in Continuous Concept Space [62.54887038032942]
  We introduce Soft Thinking, a training-free method that emulates human-like "soft" reasoning by generating soft, abstract concept tokens.<n>These concept tokens are created by the probability-weighted mixture of token embeddings, which form the continuous concept space.<n>In essence, each generated concept token encapsulates multiple meanings from related discrete tokens, implicitly exploring various reasoning paths to converge.
  arXiv  Detail & Related papers  (2025-05-21T17:29:15Z)
• Sketch-of-Thought: Efficient LLM Reasoning with Adaptive Cognitive-Inspired Sketching [64.74765550805024]
  Chain-of-Thought prompting elicits step-by-step problem solving, but often at the cost of excessive verbosity in intermediate outputs.<n>We propose Sketch-of-Thought (SoT), a prompting framework that integrates cognitively inspired reasoning paradigms with linguistic constraints.<n>SoT achieves token reductions of up to 84% with minimal accuracy loss across 18 reasoning datasets.
  arXiv  Detail & Related papers  (2025-03-07T06:57:17Z)
• Token Assorted: Mixing Latent and Text Tokens for Improved Language Model Reasoning [53.57895922042783]
  Large Language Models (LLMs) excel at reasoning and planning when trained on chainof-thought (CoT) data.<n>We propose a hybrid representation of the reasoning process, where we partially abstract away the initial reasoning steps using latent discrete tokens.
  arXiv  Detail & Related papers  (2025-02-05T15:33:00Z)
• Training Large Language Models to Reason in a Continuous Latent Space [71.0274000348354]
  We introduce a new paradigm called Coconut (Chain of Continuous Thought) to explore the potential of reasoning beyond language.<n>Instead of decoding this state into words, we feed it back to the model as the next input embedding directly in the continuous space.<n>This latent reasoning paradigm enables an advanced reasoning pattern, where continuous thoughts can encode multiple alternative next steps.
  arXiv  Detail & Related papers  (2024-12-09T18:55:56Z)
• FLARE: Faithful Logic-Aided Reasoning and Exploration [47.46564769245296]
  We introduce a novel approach for traversing the problem space using task decompositions.<n>We use the Large Language Models to plan a solution, soft-formalise the query into facts and predicates using a logic programming code.<n>Our method allows us to compute the faithfulness of the reasoning process w.r.t. the generated code and analyse the steps of the multi-hop search without relying on external solvers.
  arXiv  Detail & Related papers  (2024-10-14T19:39:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.