MUX, a simple method for high-bandwidth and compact reasoning based on distillation of discrete reasoning into continuous multiplexed tokens in a latent space, is proposed and suggests that lossless superposition as local learning targets constitutes a sufficient condition for achieving strong and efficient latent continuous reasoning.
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.
Penelope is introduced, an efficient latent-reasoning framework for pretrained decoder-only Transformers that localizes recurrent computation to a selected decoder interval and attains competitive accuracy relative to established latent-reasoning models while reducing measured inference latency.
Yutong Chen, Shouqian Shi, Xinran Liu et al.· arXiv.org· 0 citations
Chain-of-thought reasoning unfolds in discrete token space: each step is committed as text, errors propagate, and eliciting good traces presupposes traces to imitate. Reasoning instead in a model's continuous representation space - where intermediate states are vectors rather than words - sidesteps these constraints, but leaves open how those latent states should be computed. We approach this along two axes. First, we keep a large language model (LLM) frozen and use it for what it is already good at - modeling and decoding sequences - while a small auxiliary network supplies continuous latent thoughts as input. Second, we produce those latents by recurrence: a tiny recurrent reasoner refines them over many steps, decoupling the depth of computation from the size of the model, so that the latents are a product of iterative processing rather than a single forward pass. We instantiate this as Latent Recurrent Thoughts (LRT): a task-dedicated proposer supplies base latents, a recurrent reasoner refines them through bounded residual corrections, and the frozen LLM decodes the answer. On symbolic reasoning with answer supervision but no reasoning traces (Countdown-4, Sudoku) and on natural-language reasoning (HumanEval, MBPP, StrategyQA), LRT substantially outperforms prior frozen-decoder continuous-space reasoning methods under an identical decoder, prompt, data, and training budget, and outperforms non-thinking-mode chain-of-thought prompting on the same backbone at a small fraction of its inference compute.
Parason is introduced, which reveals and learns both forms of parallelism in LLM reasoning, and identifies Trial Parallelism as the majority of parallelizable reasoning computation, and it becomes increasingly dominant on hard problems.
Zhengyang Zhang, Zijian Zhang, Jiaxuan Gao et al.· 0 citations
LatentMT is introduced, the first systematic study of latent-reasoning LoopLMs for machine translation that adapts a small 2.6B-parameter backbone model with lightweight training and shows that hidden-representation differences shrink along the recurrent reasoning-step axis, supporting the observed saturation in performance.
Wei-Rui Chen, Samar M. Magdy, Chiyu Zhang et al.· arXiv.org· 0 citations
A fine-tuning-based Stratified Consistency Distillation approach that shows significant and consistent improvements in both Pass@K and the novel Equivalent Logical Similarity metrics, demonstrating the potential of advancing logical translation through consistency distillation.
Zhi-Chao Hou, Ferhat Erata, Joseph Lilien et al.· 1 citation
ReLIT (Recursive Latent Implicit Transformer), a hybrid framework that grounds deep recursive reasoning within the rich semantic representations of a foundational model, is introduced, offering a principled framework for semantically grounded implicit reasoning.
