Continuous Latent Reasoning

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5 papers in the last four weeks, up 67% on the four weeks before. 0.0% of all new papers.

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Latest papers 41

Oct 7, 2026cs.CL

Judging in Latent Space: Efficient Generative Reward Modeling via Semantics-Preserving Compression

Reward modeling often requires jointly representing and reasoning over multiple evaluation criteria, yet verbalizing this process token by token can incur substantial inference cost. Recent work on latent reasoning suggests that continuous states may support this computation more compactly. We introduce LatentGRM, a latent evaluation framework built on semantic chunking, compression, and reconstruction. By using the structure of rubric-guided evaluations to guide compression, LatentGRM learns compact continuous trajectories that support autonomous pairwise judgments without generating textual assessments. A separate interpreter reconstructs evaluation text from these trajectories, providing an offline view of the information retained under compression. Under matched training data and backbones, LatentGRM achieves competitive aggregate preference accuracy relative to explicit Supervised Fine-Tuning (SFT) judges at both 4B and 8B scales. Across four benchmark domains, LatentGRM-8B compresses evaluation trajectories by 8.9--9.2x and reduces total judge inference time by 6.1--7.0x at vote@5. Controlled rubric interventions show that criterion-dependent preference information is carried through the latent sequence. Together, these results demonstrate that continuous latent evaluation can substantially reduce inference cost while preserving competitive judgment quality.

Mingqing Yuan, Xiaobo Liang, Junwei Yang +5

Soochow University · University of Cambridge · Chalmers University of Technology +3

Reward Modeling LLM-as-a-Judge Continuous Latent Reasoning Efficient Language Model Inference

Oct 7, 2026cs.LG

Unrolled Flow Models for Reasoning

Flow matching enables language generation in few steps, but whether additional integration steps improve reasoning remains unclear. We prove that a flow parameterized by a two-layer Transformer can solve graph reachability, with the required number of integration steps increasing with the target's distance from the root. Yet, standard flow language models can fail to benefit from additional steps on reasoning tasks. We attribute this limitation to objectives that supervise each time point independently, without explicitly training successive steps to build on one another. To address this, we instead train through the model's own latent rollout over a randomly sampled subinterval of [0, 1], decoding only at the endpoint. On ProsQA, this raises accuracy to 97% and enables performance to improve with additional integration steps. For the longer rollouts required by reasoning tasks such as Sudoku and Maze, retracting the latent state onto a sphere stabilizes the dynamics and yields substantial gains over baselines with more than three times as many parameters. Sampling multiple rollouts further improves performance when paired with a parameter-free selection score, although reliable selection remains challenging for longer answers. Together, these results establish a theoretical basis for reasoning with flows and show how rollout training, stable latent dynamics, and rollout selection help realize this capacity in practice.

Faissal Izermine, Hanru Bai, Oscar Davis +1

Max Planck Institute for Intelligent Systems · ELLIS Institute Tübingen · ETH Zurich +3

Flow-Based Generative Modeling Flow Matching Continuous Latent Reasoning

Oct 7, 2026cs.CV

Spatial Latent Reasoning for Embodied Reference Understanding

Pointing-gesture visual grounding requires connecting hand geometry with the visual identity and extent of a referred object. A central challenge for continuous latent reasoning is how to organize these complementary cues into useful intermediate supervision. We propose Spatial Latent Reasoning (SLR), a framework that structures this supervision around an ordered sequence of geometric and visual states. A spatial ray state is supervised by fingertip position and pointing direction, followed by four states aligned with target-region features. To construct the visual targets, we introduce parity pooling, which applies polyphase grouping to average region tokens on four interleaved spatial supports. All states are generated recurrently during training and inference; auxiliary annotations are required only during training. On EgoPoint-Ground, the framework improves mIoU over same-backbone supervised fine-tuning by 2.8, 17.5, and 21.1 percentage points on Qwen3.5-4B, Qwen2.5-VL-7B, and Qwen3-VL-8B, respectively, with improvements on both hard subsets. On YouRefIt, it achieves 77.6% precision at IoU 0.5, a numerical margin of 5.2 percentage points over the reported state of the art under differing evaluation protocols. Ablations support joint geometric and visual supervision on the standard and similar-object sets, and favor parity over three alternative pooling operators on the standard set. These results support task-structured supervision for continuous pointing grounding. We will release the code and supporting materials.

Ling Li, Jianhui Zhong, Wei Liu +3

Tsinghua University · Dalian University of Technology · University of Science and Technology of China

Vision-Language Grounding Continuous Latent Reasoning Embodied Reasoning

Oct 7, 2026cs.AI

Efficient Reasoning with Flow Language Models

Flow Language Models (FLMs) have emerged as a continuous-state alternative to discrete diffusion language models, yet the role of their continuous representations in reasoning remains unclear. We investigate this question by comparing the reasoning efficiency of FLMs and discrete diffusion models, measured by solution accuracy under matched denoising steps. Unlike discrete diffusion, which passes categorical states between denoising steps, FLMs evolve a continuous sequence representation throughout denoising and decodes it into discrete tokens only at the end. Our theoretical analysis shows, from a superposition perspective, how information retained in these continuous states can benefit reasoning. Intermediate-state interventions provide further empirical support for this theoretical account, showing that removing information about alternative candidates reduces subsequent solution recovery. Together, these findings show that FLMs allow evidence for multiple candidates to persist and inform subsequent reasoning before a discrete answer is produced. Furthermore, our experiments on maze planning and Sudoku tasks show that FLMs achieve greater reasoning efficiency in the few-step regime: FLMs achieves higher sequence accuracy than discrete diffusion baselines at matched model sizes and small denoising steps. On maze planning tasks, FLMs can also achieve comparable accuracy with smaller models. For example, on Maze15, FLM reaches the 95% accuracy target at 64 denoising steps with 36.5% fewer parameters than MDLM. These findings point to continuous state spaces as a promising foundation for reasoning models that require fewer refinement steps.

Hanru Bai, Faissal Izermine, Oscar Davis +1

Max Planck Institute for Intelligent Systems · ETH Zurich · ELLIS Institute Tübingen +3

Efficient Language Model Reasoning Language Modeling Continuous Latent Reasoning Continuous Diffusion Language Models Algorithmic Reasoning

Oct 5, 2026cs.CV

CALR: Continuous Anchored Latent Reasoning via Render-of-Thought Compression

Visual latent reasoning compresses rendered derivations into compact intermediate states, reducing textual reasoning overhead. Existing approaches differ in how they represent these states: continuous methods avoid vocabulary constraints, whereas discrete methods improve accuracy through quantization into a finite codebook. Our analysis of representative continuous and discrete systems identifies two functional requirements: answers must rely on latent states, and those states must carry valid, problem-specific reasoning. Continuous latents influence answers despite collapsed reasoning content, whereas discrete latents retain recoverable intermediate reasoning that answer prediction largely bypasses. To address these challenges, we propose Continuous Anchored Latent Reasoning (CALR), which connects latent formation with answer use through functional anchoring. With reference latents from information-balanced compression, CALR couples latent-mediated answer supervision with derivation-level semantic anchoring: the former routes answer supervision through intermediate states, while the latter grounds their decoded content in problem-specific derivations. A parallel-to-autoregressive curriculum develops sequential reasoning by conditioning subsequent latent blocks on generated prefixes. Evaluations on five mathematical reasoning benchmarks across model families show substantial accuracy gains. Under matched budgets, CALR gains 26.0 percentage points over a comparable continuous latent reasoning method. Further analyses show that its latents support answer prediction and carry problem-specific intermediate reasoning.

Zhaoyang Wei, Bowen Jiang, Yanchao Hao +5

University of the Chinese Academy of Sciences · Tencent

Efficient Language Model Reasoning Latent Visual Reasoning Implicit Reasoning in Language Models Continuous Latent Reasoning LLM Mathematical Reasoning Latent Reasoning

Oct 5, 2026cs.LG

What Matters for Latent Reasoning with Flow Matching

Latent reasoning lets a large language model (LLM) think in a continuous space and verbalize only the answer. We argue that an effective latent thought must meet five requirements: it should be useful, helping produce the correct answer rather than merely changing it, diverse, so that resampling yields different reasoning trajectories, explainable, so that a decoded chain of thought (CoT) reflects reasoning the answer actually follows, refinable with more inference compute, and efficient, costing less than an explicit CoT at comparable accuracy. Current methods rarely meet these requirements: they learn shortcuts from the question, distill the explicit CoT into their weights, or imitate it one token at a time. We focus on flow matching in a learned latent space, the family we argue is best placed to meet them, and identify the training choices that make it work. The result is Flow-based Latent Reasoning (FLaRe), a simple recipe covering what the latent space encodes and how to shape it, where to train the flow, how to read out the answer, and a final stage of training on the model's own verified thoughts. A probe for each requirement shows that FLaRe improves on prior latent methods in all five. It also compares favorably with them on arithmetic benchmarks, while reaching 97% of the accuracy of explicit CoT at a quarter of its latency.

Yassine Ouali, Adrian Bulat, Georgios Tzimiropoulos

Samsung AI Cambridge · Technical University of Iasi · Queen Mary University of London

Flow Matching Efficient Language Model Reasoning Continuous Latent Reasoning Latent Reasoning

Sep 28, 2026cs.AI

Principled Thoughts for Latent Recursive LLM Systems

Large language models can reason in continuous space instead of decoded text, by recurring on their own hidden states or by passing those states between agents, while training supervises only the Cross-Entropy (CE) of the final decoded answer and does not constrain the thought. Theoretical and empirical analyses establish and confirm four failures of CE-only training that lead to a lower probability of the correct answer such as collapsing thoughts across distinct questions and retaining irrelevant information. We introduce REST (REpresentation-Supervised Thoughts), a training objective that turns four properties of a valid thought representation (causality, minimality, separability, and stability) into differentiable losses added to CE. We instantiate it in latent single-agent and multi-agent systems, without architectural changes or added parameters at inference. Across 7 benchmarks spanning mathematics, science, medicine, and code generation, with the same training data, compute, and latent budget, REST increases accuracy over CE-only training across agent settings and model sizes by up to 7.5 percentage points and convergence on a final answer by 30%. Furthermore, REST thoughts encode more of what is required to achieve the correct answer, and decoding them better recovers the intended output of the agent, which makes latent communication easier to interpret. Project Website: https://fard-lab.github.io/REST

Fahd Seddik, Fatemeh Fard

FARD Lab, University of British Columbia, Okanagan, Canada

Continuous Latent Reasoning Multi-Agent LLMs LLM Training Latent Reasoning Recursive Language Models

Sep 28, 2026cs.AI

Reasoning with Continuous Latent Diffusion

Continuous diffusion generates complete reasoning solutions through iterative refinement in latent space. We introduce the Continuous Embedding Diffusion Reasoner (CEDR), an ELF-based training and inference recipe. Our experiments show that accurate decoding alone does not ensure strong reasoning performance. We therefore learn compact representations from multiple layers of a strong autoregressive teacher. Their decomposition also enables asynchronous denoising at different rates. We show that prompt encodings need only preserve the information required for the correct text-conditional score, rather than exactly match teacher features, and use a staged curriculum to learn a compact prompt encoder that replaces the teacher Transformer at inference. We adapt DiffusionNFT to learned self-conditioning guidance and incorporate gold-solution endpoints to supplement sparse rewards. Our supervised models outperform reported results from recent continuous-diffusion baselines at comparable backbone scales on mathematical reasoning and HumanEval code generation. With a 638M-parameter denoising backbone and learned prompt conditioning, post-NFT CEDR-L achieves 63.74% pass@1 on GSM8K and 24.6% on MATH500 at 64 denoising steps, and 32.85% on HumanEval and 30.18% on HumanEval+ at 128 denoising steps. Code will be available at: https://github.com/chengxiang/CEDR.

Xiang Cheng

Duke University Department of Electrical and Computer Engineering

Numerical Reasoning in Language Models Code Generation Continuous Latent Reasoning Diffusion Language Models Continuous Diffusion Language Models

Sep 27, 2026cs.AI

Next Thoughts Are Distributions: Generative Autoregressive Reasoning in the Latent Space

Reasoning problems often admit multiple valid ways to proceed. Continuous reasoning promises to move computation beyond language tokens into a more compact latent space, but representing several plausible ways to think next remains difficult. We introduce Autoregressive Thought Flow (ATF), which models the next continuous thought as a multimodal distribution. A causal autoregressive model performs the reasoning computation, while a lightweight diffusion head generates a plausible next thought from the resulting condition. The sampled thought is fed back into the model, allowing continuous reasoning to unfold for a variable number of steps while preserving the pretrained backbone. Across mathematical reasoning tasks, ATF improves accuracy with compact latent traces and benefits from reinforcement learning and additional test-time thinking. Multi-sample evaluation shows broader solution coverage, indicating that its multimodal predictions capture useful diversity among reasoning paths. Our results suggest that continuous reasoning is more effective when multiple possible next thoughts remain available rather than being collapsed into a single prediction.

Yang Li, Yi Wang, Shiyuan Huang +3

Rutgers University · Amazon · University of Illinois at Urbana-Champaign

Numerical Reasoning in Language Models Continuous Latent Reasoning Latent Reasoning Latent CoT Reasoning

Sep 7, 2026cs.CL

A*-Thought-V2: Efficient Latent Reasoning via Geometric Dynamics of LLM

Chain-of-Thought (CoT) improves the reasoning ability of Large Language Models (LLMs) but incurs substantial computation and context costs. Existing methods either lose intermediate information through hard pruning or lack a principled criterion for continuous compression. We present A*-Thought-V2, a geometric dynamics of LLM guided framework that models CoT as a hidden-state trajectory and replaces hard deletion with an explicit-implicit interleaved latent architecture. After projecting question, step, and solution representations into a 3D PCA space, it measures alignment between each local transition and global question-to-solution direction. Aligned steps remain explicit text, whereas deviating steps are compressed into continuous latent tokens. Directional angles capture both local semantics and reasoning dynamics: small angles indicate direct execution and answer formation, while large angles more frequently involve checking, correction, and branch exploration; their temporal variation reveals exploration, convergence, and refinement stages. To train this architecture, we introduce stepwise embedding forcing, which pools each redundant step into a single latent embedding, and label forcing, which supervises that latent token with a soft multi-modal vocabulary distribution instead of a hard one-hot label. Experiments on Qwen3.5-9B and Qwen3.6-27B across six in-domain and out-of-domain benchmarks show that A*-Thought-V2 improves average accuracy by up to 2.6% while reducing response length by up to half, increasing Accuracy per Computation Unit by 2.29

\times

, and reducing preprocessing and training time by 94.6% and up to 80.3%, respectively. Representation analyses suggest that latent states form a compact region distinct from textual states, while higher entropy at latent-token positions reflects broader soft targets that encourage richer step-level feature learning.

Xiaoang Xu, Siyuan Liu, Shuo Wang +13

Beijing University of Posts and Telecommunications · OpenBMB · The Hong Kong Polytechnic University +2

Efficient Language Model Reasoning Continuous Latent Reasoning Efficient Language Model Inference Representation Geometry in Language Models CoT Compression Latent Reasoning

Sep 7, 2026cs.LG

Think Wider: Mitigating Latent Rank Collapse in Implicit Chain-of-Thought Reasoning

Chain-of-thought (CoT) reasoning improves the reasoning ability of large language models by introducing intermediate computation, but explicit rationales increase decoding length, latency, and context cost. Implicit CoT offers a more efficient alternative by moving intermediate reasoning into continuous latent states. However, latent reasoning can be unstable: successive latent states may become overly similar and collapse toward a shared dominant direction, reducing the diversity of the reasoning trajectory. In this work, we identify

\textit{latent rank collapse}

and propose

\textbf{WIDER}

, a lightweight spectral regularizer for implicit CoT. During training, WIDER estimates the shared direction of each latent trajectory and penalizes projections onto this direction, encouraging latent states to span a broader representational subspace. The method is plug-and-play and leaves the backbone model, latent schedule, and inference-time decoding procedure unchanged. We further formulate this collapse as a geometric bottleneck in implicit reasoning, casting its mitigation as a training-time regularization problem rather than an inference-time decoding change. Extensive experiments show that WIDER improves matched implicit CoT baselines, while mechanistic analyses reveal higher effective rank, lower dominant-direction energy, and reduced redundancy among latent steps. These results highlight latent subspace utilization as an important factor for efficient continuous reasoning, providing a geometric perspective for analyzing and improving implicit CoT. Code is available at https://github.com/whitesweater/WIDER.

Yuwen Hao, Menglin Yang

The Hong Kong University of Science and Technology (Guangzhou)

Spectral Regularization Continuous Latent Reasoning Representation Geometry in Language Models Latent CoT Reasoning

Sep 2, 2026cs.LG

The Dynamics of Continuous Mixture Collapse in Language Models

LLMs latent-state reasoning methods replace discrete intermediate tokens with continuous states, such as weighted mixtures of token embeddings, to retain multiple possible reasoning directions rather than committing to one. Yet pretrained language models often fail to preserve these mixtures. We study why through a combination of theoretical analysis and controlled empirical investigations on a variety of models. We identify three independent, distinct sources of failure. First, transformer architectures already distort mixture geometry, and training substantially amplifies this effect. Moreover, the failure can occur even if the model transports mixtures perfectly linearly: the softmax readout and autoregressive feedback form a dynamical system that either amplifies small differences until one component of the mixture dominates or contracts different mixtures until they become indistinguishable. We verify this theoretical prediction empirically: the observed transition between contraction and amplification occurs near the theoretical threshold derived by our analysis, and pretrained-model rollouts lie predominantly on the amplifying side. Finally, we generalize to mixtures of many components and show that exact preservation generally requires context-dependent correction, whose required dimensionality can grow with the number of components.

Ali Backour

Massachusetts Institute of Technology Cambridge, MA 02139

Continuous Latent Reasoning Representation Geometry in Language Models

Sep 1, 2026cs.AI

Latent Recurrent Thoughts: Recurrent Refinement of Proposed Latents for Reasoning with Frozen LLMs

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.

Zhaoliang Chen, Jie Fu

Emory University · IQuest Research

Efficient Language Model Reasoning Continuous Latent Reasoning LLM Reasoning Latent CoT Reasoning

Aug 31, 2026cs.LG

A Model with No Head and Many Thoughts

Large language models decode by projecting hidden states through a large vocabulary head at every step. This operation is computationally costly and forces all reasoning to be expressed in discrete tokens. We introduce Soft Latent Thinking, a method that replaces the LM head during reasoning with a lightweight projector, enabling autoregressive rollout in embedding space where reasoning steps remain continuous rather than tokenized. Experiments on DeepSeek-Qwen-1.5B and LLaMA-3.2-3B show that Soft Latent Thinking consistently improves pass@k across all k while reducing per-step compute during chain-of-thought. Our method achieves the highest pass@32 among all soft-thinking approaches, demonstrating that effective reasoning can be carried out in continuous space without discrete token generation.

Nikita Koriagin, Yaroslav Aksenov, George Bredis +3

1Yandex · 2T-Tech

Efficient Language Model Reasoning LLM Inference Acceleration Continuous Latent Reasoning LLM Reasoning

Aug 8, 2026cs.AI

Think Deep, Speak Once: Relit, A Recursive Latent Implicit Transformer Framework

Chain-of-Thought (CoT) prompting has become the dominant paradigm for eliciting reasoning in Large Language Models (LLMs), yet it creates substantial computational overhead by forcing models to externalize intermediate reasoning steps as discrete tokens. Recent latent reasoning approaches attempt to internalize this process within continuous hidden states. One of the latest advancements in the field of latent reasoning, Tiny Recursive Models (TRMs) excel at symbolic reasoning but struggle to preserve semantic coherence in natural language settings. To bridge this gap, we introduce ReLIT (Recursive Latent Implicit Transformer), a hybrid framework that grounds deep recursive reasoning within the rich semantic representations of a foundational model. ReLIT augments a frozen LLM backbone (TinyLlama-1.1B) with a lightweight, trainable recursive block that iteratively refines its latent thinking (z) before committing to a final output, structurally solving linguistic intuition from algorithmic processing and enabling "deep thinking" via gradient-isolated recurrent loops without the latency of explicit token generation. Empirically, ReLIT achieves high parameter efficiency on the GLoRE logical reasoning benchmark, matching or outperforming significantly larger models on challenging tasks such as ProofWriter and RuleTaker despite minimal supervision. These results demonstrate that reasoning capability can be scaled efficiently through recurrent depth rather than parameter width, offering a principled framework for semantically grounded implicit reasoning.

Abhishek Panwar, Maheep Singh, Saksham Bansal

Indian Institute of Technology Roorkee, India

Continuous Latent Reasoning Efficient Language Model Inference LLM Reasoning Latent Reasoning Recursive Language Models

Aug 3, 2026cs.LG

GradCuit: Credit-Assigned Gradient Flow Enables Robust and Interpretable Test-Time Latent Reasoning

Optimization-based latent reasoning improves large language model outputs by optimizing instance-specific continuous states at test time while keeping model parameters frozen. Existing methods, however, typically connect these states to the reasoning trajectory through decoded tokens, making sequence-level credit assignment indirect and obscuring how latent updates shape subsequent reasoning. We introduce GradCuit (gradient through circuit), which inserts optimizable latent states at a selected Transformer layer between the hidden representations of the prompt and the generated continuation. Causal self-attention provides every continuation-token log-probability with a differentiable path to every preceding latent state through the remaining Transformer blocks, enabling reward-weighted gradients from the entire continuation to be assigned directly to the latents. Across five instruction-tuned backbones, three reasoning benchmarks, and two answer formats, GradCuit achieves an average accuracy of 64.5%, outperforming chain-of-thought prompting by 6.6 percentage points and the strongest competing method by 2.4 points. GradCuit also demonstrates greater robustness: across seven learning-rate settings, it consistently outperforms LatentSeek while reducing the standard deviation of accuracy from 1.53 to 0.82, and even its random-walk variant remains competitive with LatentSeek. For interpretability, token-level gradient attribution reveals that latent influence concentrates on reasoning-connector tokens, while layer analysis identifies early-to-middle Transformer layers as the most effective optimization space. By directly optimizing internal reasoning from outcome feedback, GradCuit opens a new axis of robust and interpretable test-time scaling, where LLMs adapt how they reason rather than merely regenerate, sample, or rerank outputs.

Zhaoxin Yu, Qi Shen, Hengli Li +4

NLCo Lab, Beijing Institute for General Artificial Intelligence · School of Artificial Intelligence, Beijing University of Posts and Telecommunications · School of Artificial Intelligence for Science, Peking University

Test-Time Optimization LLM Interpretability Continuous Latent Reasoning Language Model Robustness LLM Reasoning Latent Reasoning

Aug 3, 2026cs.AI

Latent Thought Credit: Multi-Answer Credit Assignment for Latent Reasoning

Latent reasoning allows language models to carry out intermediate reasoning in continuous latent representations rather than fully externalizing it as discrete chains of thought. However, assigning credit to such latent thoughts from answer-only rewards is difficult: a single final answer mixes thought quality with answer-sampling noise. We propose \textbf{Latent Thought Credit (LTC)}, a hierarchical credit-assignment framework for latent reasoning. For each prompt, LTC samples multiple latent thoughts, fixes the context after each thought, and estimates thought-level expected reward by averaging rewards over multiple answers generated from that fixed context. LTC uses thought-level advantages to optimize the latent-thought phase, answer-level advantages to optimize the answer phase, and an advantage-weighted thought-matching objective that helps the policy reproduce high-credit latent thoughts. We instantiate LTC in a GRPO-style on-policy training framework and evaluate it across mathematical reasoning and STEM multiple-choice tasks. LTC achieves the best average accuracy among the compared methods, while ablations and fixed-context diagnostics show that multi-answer estimation reduces reward-estimation error and mitigates ambiguous or incorrect thought-level credit.

Xuyang Zhao, Liting Zhang, Zichen Xu +4

TMCC, College of Computer Science, Nankai University, Tianjin, China · Lingxi (Beijing) Technology Co., Ltd.

Numerical Reasoning in Language Models RL for Language Model Reasoning Credit Assignment in RL Continuous Latent Reasoning Latent Reasoning

Jul 23, 2026cs.LG

The Weight of Silence: A Causal Case for Weights Over the Scratchpad in Latent Chess Reasoning

Latent, or silent, reasoning lets language models carry out intermediate computation in continuous vector space instead of words, and is widely assumed to function as an internal scratchpad the model consults during inference. Whether that assumption survives reinforcement learning has not been tested directly: existing causal analyses of latent reasoning are confined to math and logic tasks, comparing reliance on thoughts within one checkpoint, never before and after RL. We train a chess-playing model through a staged latent-reasoning curriculum followed by reinforcement learning, and find legality climbs monotonically to 61% (from a 48% pre-RL baseline) while checkmate confabulation is eliminated entirely. To locate this gain, we run a six-condition causal intervention suite on the same model before and after RL: substituting or noising the thought vectors leaves performance unchanged, ablating them costs only mild degradation, and only exact-zero vectors cause collapse. This robustness gap is itself the finding: under exact-zero corruption, legality collapses to 1% pre-RL versus 9% post-RL, a gap that survives correction across the full battery. A 10x-larger replication of the post-RL checkpoint's own battery confirms this: removing the thoughts, with or without restoring sequence length, also reaches significance; substitution and noise remain indistinguishable from baseline. RL appears to add robustness to disruption, not reliance on thought content. These results push back against the field's default assumption that latent thoughts function as an actively consulted inference-time scratchpad, and instead indicate latent reasoning's principal effect here is shaping the model's parameters during training. We also demonstrate a working RL gain in chess, where multiple groups report the same latent-reasoning-plus-RL recipe failing to improve accuracy over SFT.

Ishan S. Kshirsagar

Independent Researcher

RL for Language Model Reasoning Continuous Latent Reasoning Causal Interventions in Language Models Language Model Robustness Latent Reasoning

Jul 22, 2026cs.CL

SLPO: Scaling Latent Reasoning via a Surrogate Policy

Reinforcement learning with verifiable rewards has become the predominant recipe for eliciting test-time scaling in explicit Chain-of-Thought reasoners. Yet this scaling path remains computationally costly, since every intermediate step must be decoded as a language token. Latent reasoning instead carries intermediate computation as continuous vectors and already matches or surpasses explicit CoT at far shorter horizons. Despite this promise, latent reasoners remain largely imitation-bound, while explicit CoT has already moved past imitation via outcome-reward RL. Latent trajectories lack a tractable per-step likelihood and an adaptive stopping interface under fixed thinking budgets, so outcome rewards cannot elicit latent test-time scaling. We introduce Surrogate Latent Policy Optimization (SLPO) to bring outcome-reward RL to autoregressive latent reasoners: an empirical surrogate policy density over latent transitions for trajectory-level credit assignment, and a correctness-supervised stopping head that outcome-reward optimization refines into a variable-horizon policy. Across continuous and soft thinking settings, SLPO improves Pass@

k

under parallel sampling and allocates longer latent computation to harder instances with higher deterministic accuracy.

Runyang You, Zhiyuan Liu, Yongqi Li +1

The Hong Kong Polytechnic University · Sichuan University · Work done as an intern at PolyU.

Reinforcement Learning RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Continuous Latent Reasoning Adaptive Computation Latent Reasoning

Jul 18, 2026cs.AI

Training Continuous Chain of Thought Models: A Tale of Two Regimes

Continuous Chain-of-Thought methods replace verbose reasoning traces with a short sequence of dense latent representations. Earlier continuous CoT methods indirectly supervise the latent representations such that its final state match that of verbose reasoning traces, requiring autoregressive, slow generation during training. We introduce C-MTP, a simpler, faster direct supervision approach that models each latent as an average of the embeddings in the CoT traces to be compressed. Our approach outperforms a prior direct supervision method that approximates the distribution of compressed tokens, and performs competitively to slower indirect supervision approaches in existing evaluation setup with simplified CoT traces (less than 100 tokens). Lastly, we extend the evaluation of Continuous CoT methods to complex tasks with longer reasoning traces (

\ge

few hundreds reasoning tokens). We find both direct and indirect supervision training methods perform poorly (roughly 65% performance drop) in this setting, revealing the limitations of current continuous CoT methods. The code and checkpoints are released at https://github.com/Varun221/cmtp_research

Varun Yerram, He He, Eunsol Choi

Center for Data Science, New York University

CoT Reasoning Continuous Latent Reasoning LLM Training CoT Compression Latent Reasoning

Jul 7, 2026cs.LG

Final Checkpoints Are Not Enough: Analyzing Latent Reasoning Faithfulness Along Training Trajectories

Latent reasoning performs multi-step inference in continuous hidden states, promising more compact and efficient reasoning. However, these opaque states raise a question of faithfulness: whether the latent reasoning steps drive the final answer. Prior work studies this question at selected checkpoints and reports several unfaithful behaviors. This endpoint view leaves how evidence of faithfulness evolves during training unexamined. We track behavioral and activation-based evidence across training using verified counterfactual edits and interventions on the latent reasoning states. We find that high task accuracy can coexist with low counterfactual responsiveness: as accuracy improves, responsiveness can decline, and different latent reasoning approaches follow distinct trajectories. On ProsQA, output sensitivity to norm-noise replacement declines alongside counterfactual responsiveness, although the result depends on the replacement. Across separately trained binary-choice and open-ended GSM settings, intervention sensitivity follows opposite trajectories. These results show that evaluating only a final checkpoint can obscure both when counterfactual responsiveness changes and what the latent states contribute.

Hengyu Jin, Shu Yang, Di Wang

Tongji University · Provable Responsible AI and Data Analytics (PRADA) Lab · King Abdullah University of Science and Technology

CoT Faithfulness Continuous Latent Reasoning Causal Interventions in Language Models Latent Reasoning Latent CoT Reasoning

Jul 1, 2026cs.CV

Multimodal Continuous Reasoning via Asymmetric Mutual Variational Learning

Multimodal Large Language Models (MLLMs) are often constrained by a language-space bottleneck, forcing complex visual reasoning into discrete tokens which can lose perceptual nuance. A promising alternative is continuous latent reasoning, where the goal is to discover implicit reasoning pathways that bridge the multimodal query and the final answer. However, this introduces a severe train-inference mismatch: a training-time posterior, conditioned on the ground-truth answer, can exploit answer-dependent shortcuts. Standard variational training then forces the inference-time prior to mimic a posterior that has access to information unavailable at test time, leading to poor performance. To address this, we propose Asymmetric Mutual Variational Learning (AMVL), a framework that resolves this mismatch via a bidirectional calibration objective. A forward KL divergence trains the target-agnostic prior to match the posterior, while a novel reverse KL divergence simultaneously regularizes the posterior, preventing it from collapsing into inference-incompatible regions and mitigating this ``answer leakage''. We provide theoretical analysis formalizing this leakage as prior contamination and prove that our dual-KL objective reduces it. We instantiate AMVL in a latent-integrated MLLM and show that it consistently outperforms strong discrete and latent-reasoning baselines, improving the average score on the complex BLINK benchmark by +10.83 and achieving gains of up to +32.00 on individual reasoning tasks, with analyses confirming improved latent-space stability.

Shijie Li, Yilin Gao, Siyuan Yang +7

Shanghai Jiao Tong University · Ant Group

Multimodal Large Language Models Latent Visual Reasoning Continuous Latent Reasoning Multimodal Foundation Models Variational Inference Latent Reasoning+1

Jun 30, 2026cs.LG

Bridging the Gap Between Latent and Explicit Reasoning with Looped Transformers

Language models typically reason via explicit chain-of-thought (CoT), generating intermediate steps token-by-token. Latent CoT offers an alternative: it performs multi-step reasoning in the model's hidden states, replacing decoded tokens with continuous representations for greater efficiency. However, existing latent CoT methods underperform explicit CoT beyond 1B parameters, and the gap widens with scale. Looped, or recurrent-depth, Transformers, which reuse their weights to increase computation depth without adding parameters, are a natural fit for latent reasoning. We therefore ask whether looped Transformers can bridge this gap. We answer affirmatively with a simple recipe: a looped padded Transformer that processes K latent blocks in parallel for R iterations, with a cross-entropy loss on each latent position's gold CoT-step token, similar to explicit CoT supervision. We instantiate it as LOTUS (Looped Transformers with parallel supervision on latents). LOTUS is, to our knowledge, the first latent-CoT method to bridge the gap to explicit CoT at the 3B scale, while cutting thought-phase latency by 2.5x-6.9x from compact math expressions to natural language. Projecting LOTUS's post-loop latents through the base LM head recovers the gold reasoning steps and even surfaces alternative valid intermediate steps, evidence that its latent space is interpretable and CoT-aligned. Ablations confirm that both the looped backbone and the parallel supervision on gold CoT tokens are essential. Code is available at https://github.com/yingfan-bot/lotus.

Ying Fan, Anej Svete, Kangwook Lee

Microsoft Research · 2ETH Zürich · 3KRAFTON +1

CoT Reasoning Recurrent Transformers Continuous Latent Reasoning Efficient Language Model Inference Latent CoT Reasoning

Jun 29, 2026cs.CL

Why Struggle with Continuous Latents? Interpretable Discrete Latent Reasoning via Rendered Compression

Large language models achieve high reasoning performance via explicit chain-of-thought and reinforcement learning, but require long output sequences and extended inference time. Latent reasoning reduces this cost by shifting computation into a latent space; however, continuous latent methods are hard to train, suffering from unstable and uninterpretable reasoning trajectories. We argue these issues stem from a misalignment between continuous-space reasoning and discrete symbolic supervision, as continuous states lack explicit anchors for step-by-step alignment. To resolve this, we propose \textbf{Discrete Latent Reasoning~(DLR)}, the first method that converts continuous latent states into explicit discrete tokens. Inspired by render-based compression, we render textual chains of thought into images, extract visual features, and construct a discrete latent vocabulary via clustering-based fine-tuning. Expanding the vocabulary and output head enables standard autoregressive modeling over both natural language and latent tokens, supporting pretraining alignment, SFT, and RL. Experiments on five reasoning benchmarks and two model series~(Qwen3-VL and LLaMA-3) confirm that \textbf{DLR} outperforms prior latent reasoning baselines with up to \textbf{20

\times

compression}. Furthermore, the learned latent trajectories retain an interpretable semantic structure. Overall, discrete latent tokens provide a controllable and interpretable basis for efficient latent reasoning.

Shuochen Chang, Qingyang Liu, Shaobo Wang +8

Shanghai Jiao Tong University · Tongji University

LLM Interpretability Efficient Language Model Reasoning Continuous Latent Reasoning Efficient Language Model Inference LLM Reasoning Latent Reasoning

Jun 18, 2026cs.LG

What Makes Effective Supervision in Latent Chain-of-Thought: An Information-Theoretic Analysis

Latent Chain-of-Thought (CoT) internalizes reasoning within continuous hidden states, offering a promising alternative to verbose discrete reasoning traces. However, robust latent reasoning remains difficult because outcome supervision provides weak learning signals and leaves latent trajectories prone to semantic drift. In this work, we analyze Latent CoT from an information-theoretic perspective and identify this failure as a dual collapse: gradient attenuation along the optimization path and representational drift in the latent space. We further decompose process supervision into two complementary dimensions: Trajectory Supervision, which injects dense stepwise reasoning signals, and Space Supervision, which preserves the semantic structure of the latent manifold. Our analysis shows that rigid geometric compression can collapse the reasoning space, whereas generative reconstruction provides a more flexible semantic anchor that better preserves information capacity. To measure these effects, we introduce the Unified Latent Probe (ULP), which quantifies the mutual information between latent trajectories and explicit reasoning steps. Experiments reveal a clear Information-Performance Binding: reasoning accuracy depends on the information fidelity preserved in the latent chain. These findings provide a principled framework for latent reasoning supervision and suggest shifting from geometric imitation toward mutual information maximization. Our code is available at this repository.

Xinghao Chen, Chak Tou Leong, Wenjin Guo +3

Ningbo Institute of Digital Twin, Eastern Institute of Technology, Ningbo, China · Department of Computing, The Hong Kong Polytechnic University, Hong Kong, China.

Continuous Latent Reasoning Process Supervision Representation Geometry in Language Models Latent CoT Reasoning

Jun 15, 2026cs.CL

Tyler: Typed Latent Reasoning for Language Models -- When to Think, What to Compute, and How Much to Allocate

Chain-of-thought (CoT) prompting improves reasoning in large language models (LLMs) by externalizing intermediate computation as discrete text tokens, but this textual interface also introduces redundancy and inference overhead. Latent reasoning offers a promising alternative by carrying part of the computation in continuous representations. However, existing methods typically predefine when latent computation is invoked and how it is allocated during decoding, leaving a key problem unresolved: when to invoke latent computation, what type of computation to perform, and how much budget to allocate. We propose \textbf{Ty}ped \textbf{L}at\textbf{e}nt \textbf{R}easoning (Tyler), a typed and budget-aware framework for latent reasoning during autoregressive decoding. Tyler learns a policy that, at each decoding step, chooses between emitting a text token and switching to a latent computation module specialized for a particular reasoning function. Once invoked, an operator maps the current reasoning state into latent tokens that support global planning, local state updates, or reusable procedural abstraction. Across extensive experiments on three backbone LLMs, Tyler improves accuracy by up to 14.49 points over CoT and by up to 4.30 points over the strongest competing baseline. It further generalizes across diverse reasoning domains and achieves the best final-stage performance with the lowest forgetting.

Hanyu Lin, Min Cai, Jiawei Wen +1

1Shenzhen University · University of Alberta

Language Model Decoding Efficient Language Model Reasoning Continuous Latent Reasoning LLM Reasoning Adaptive Computation Latent Reasoning

Jun 15, 2026cs.AI

Latent Thought Flow: Efficient Latent Reasoning in Large Language Models

Large Language Models (LLMs) increasingly rely on intermediate reasoning, yet explicit Chain-of-Thought (CoT) suffers from a linguistic space bottleneck: each thought must be decoded into tokens, causing high inference overhead. Latent reasoning moves deliberation into continuous space, but existing methods mostly learn deterministic or reward-maximizing paths, lacking a principled way to allocate probability across trajectories with different correctness and costs. We propose Latent Thought Flow (LTF), which models reasoning as variable-length continuous trajectories and trains a sampler to match a reward-induced posterior over answer quality and computation cost. We instantiate this with a continuous GFlowNet using stochastic latent transitions. To handle sparse answer supervision, we introduce an Entropy-Weighted Subtrajectory Balance objective for intermediate rewards and a reference-prior regularizer to anchor exploration. Experiments under finetuning and transfer learning settings show that LTF outperforms explicit CoT and latent reasoning baselines, improving accuracy by 9.5% while reducing reasoning length by 27.2% on average compared with strong latent reasoning baselines.

Xiandong Zou, Jing Huang, Jianshu Li +1

Singapore Management University · Ant Group

RL for Language Model Reasoning Efficient Language Model Reasoning Generative Flow Networks LLM Inference Acceleration Continuous Latent Reasoning Latent Reasoning

Jun 10, 2026cs.CL

Observable Patterns Are Not Explanations: A Causal-Geometric Analysis of Latent Reasoning Models

Latent reasoning models (LRMs) replace explicit chain-of-thought with continuous thoughts. Recent work treats observable latent-state patterns, such as BFS-like frontiers and decodable arithmetic computation, as evidence for internal reasoning mechanisms. Evaluating two LRMs (Coconut and CODI) against controls lacking the proposed recurrence or curriculum, we find these patterns also appear in the controls and do not always causally affect behavior. Causal interventions reveal that latent-thought utilization is not binary but graded, scaling with a thought's causal effect on model behavior. Geometric analyses reveal this effect concentrates in low-rank directions whose step-to-step geometry grows more structured as their behavioral influence increases. Latent thoughts should therefore be treated as hidden computation, not hidden explanation: decodability, attention, or static structure alone cannot establish mechanism. LRM interpretability thus requires matched controls and causal tests.

Darpan Aswal, Thomas Palmeira Ferraz, Yongxin Zhou +1

Université Grenoble Alpes, CNRS, Grenoble INP, LIG · Université Paris-Saclay · NAVER LABS Europe

Continuous Latent Reasoning Causal Interpretability Large Reasoning Models Latent Reasoning Latent CoT Reasoning

Jun 8, 2026cs.LG

Dropout-GRPO: Variational Stochasticity for Continuous Latent Reasoning

Group Relative Policy Optimization (GRPO) relies on the diversity of

K

rollouts within each group; otherwise, the group-mean advantage

A^{(k)} = r^{(k)} - μ_r

collapses to zero. This presents a structural challenge for latent-reasoning models like Coconut, which feed continuous hidden states recurrently in place of discrete chain-of-thought tokens. Because the latent phase is inherently deterministic given the parameters and prompt, multiple rollouts produce identical trajectories, stalling GRPO's progress. Consequently, applying group-relative reinforcement learning to continuous latent reasoning has proven difficult. To address this, we propose sourcing the necessary stochasticity through structured dropout. By applying a single Bernoulli mask held constant across all latent recurrence steps for a given rollout, we generate essential trajectory variance. This shared mask effectively treats each rollout as a posterior sample from a variational distribution over parameters, allowing GRPO to optimize the expected reward of a Bayesian model-average policy. We provide both theoretical justification for this method -- including unbiasedness, variance reduction, and the well-definedness of the latent gradient -- and empirical validation. On GSM8K, dropout-GRPO improves a Coconut baseline from

27.29\%

to

29.01\%

pass@1, demonstrating the viability of GRPO learning for latent-reasoning models. Our work positions this as a practical, theoretically grounded approach for post-training latent-reasoning LLMs.

Wooil Jung

RL for Language Model Reasoning Group Relative Policy Optimization Continuous Latent Reasoning RL Post-Training Latent Reasoning

Jun 5, 2026cs.AI

Why Limit the Residual Stream to Layers and Not Tokens? Persistent Memory for Continuous Latent Reasoning

Large language models (LLMs) have demonstrated remarkable reasoning abilities on mathematical and multi-hop planning tasks. The CoCoNuT (Chain of Continuous Thought) paradigm~\cite{hao2024coconut} extends this by enabling models to reason in latent space, exploring multiple reasoning paths simultaneously rather than committing to a single chain early on. However, we identify a limitation we term the \textbf{concept bottleneck}. At each reasoning pass, intermediate hidden states are overwritten, causing the model to lose critical facts computed in earlier steps as reasoning depth increases. We observe this empirically. On HotpotQA, vanilla CoCoNuT (10.4% EM) fails to improve over the CoT baseline (11.0% EM), and performance degrades with curriculum depth on GSM8K. To address this, we propose \textbf{AGCLR} (Adaptive Gated Continuous Latent Reasoning), which augments CoCoNuT with a \textit{Gated Concept Stream}. A persistent residual memory maintained across all reasoning passes, controlled by three learned gates: a \textit{write} gate that commits intermediate facts to memory, a \textit{read} gate that retrieves relevant prior states, and a \textit{forget} gate that prunes irrelevant context. Evaluated on GSM8K, HotpotQA, and ProsQA using GPT-2 as our base model, AGCLR achieves consistent improvements across all types of datasets. With the performance gap compounding as curriculum depth increases, directly resolving the concept bottleneck. Code available at https://anonymous.4open.science/r/JJJJ/README.md

Mujtaba Farhan, Maheep Chaudhary

1Algoverse AI Research · 2Independent

Memory-Augmented Language Models Persistent Memory for Language Models Mathematical Reasoning Continuous Latent Reasoning Latent Reasoning