Sliding-window transformers without positional encodings are Turing complete because the sliding window breaks permutation symmetry and suffices to simulate Post machines via a constant-size histogram state.
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Training Large Language Models to Reason in a Continuous Latent Space
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abstract
Large language models (LLMs) are typically constrained to reason in the language space, where they express the reasoning process through a chain-of-thought (CoT) to solve complex problems. However, the language space may not always be optimal for reasoning. Most word tokens primarily ensure textual coherence and are not essential for reasoning, while some critical tokens require complex planning and pose challenges to LLMs. To explore the potential of reasoning beyond language, we introduce a new paradigm called Coconut (Chain of Continuous Thought). Coconut utilizes the last hidden state of the LLM as a representation of the reasoning state, termed "continuous thought." Instead of decoding this state into words, we feed it back to the model as the next input embedding directly in the continuous space. This latent reasoning paradigm enables an advanced reasoning pattern, where continuous thoughts can encode multiple alternative next steps, allowing the model to perform a breadth-first search (BFS) rather than committing prematurely to a single deterministic path as in CoT. Coconut outperforms CoT on logical reasoning tasks that require substantial search during planning and achieves a better trade-off between accuracy and efficiency.
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- abstract Large language models (LLMs) are typically constrained to reason in the language space, where they express the reasoning process through a chain-of-thought (CoT) to solve complex problems. However, the language space may not always be optimal for reasoning. Most word tokens primarily ensure textual coherence and are not essential for reasoning, while some critical tokens require complex planning and pose challenges to LLMs. To explore the potential of reasoning beyond language, we introduce a new paradigm called Coconut (Chain of Continuous Thought). Coconut utilizes the last hidden state of t
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representative citing papers
L-layer transformers under Log-ICoT curriculum provably learn k-parity with poly(n) samples and log k stages, matching explicit CoT efficiency without inference overhead.
Active lifting of data distributions via latent-sequence sampling and max-rate uncertainty reduction formally derives slow-thinking LLMs and places them on representation and sampler hierarchies that can be climbed.
DiscoLoop adds a decoded token-embedding channel to looped transformers, fixing a representation mismatch that limited implicit multi-hop reasoning and improving OOD generalization.
In-distribution sampling across 25 models and controlled interventions with DAG-verified content show that semantic reasoning and validation content, not token count, drive CoT gains.
LBR performs token-level test-time scaling via local branch routing on hidden states, enabling end-to-end RL training and improving Pass@1 and Pass@32 on math benchmarks over CoT and RLVR baselines.
A simplified one-layer transformer provably learns parities first with explicit CoT supervision then internalizes to direct computation as CoT tokens are removed.
PearlVLA achieves SOTA on LIBERO by separating VLM representations into visual grounding and an iterative latent plan branch refined via world model queries and RefineNet with process-reward RL.
Heterogeneous agents achieve dense latent KV-cache communication via lightweight cross-model transformation and two-phase training, outperforming text at lower compute in context-aware settings and enabling context-unaware transfer.
SWITCH uses explicit <swi> and </swi> boundary tokens to make latent chain-of-thought compatible with on-policy RL (GRPO) and open to causal mechanistic probing, outperforming prior hidden-state recurrence methods.
CaLIR learns continuous latent intent states guided by product category hierarchies for generative retrieval, combining hierarchical reasoning and dynamic prefix tries to balance effectiveness and low-latency inference on multilingual e-commerce data.
Future-L1 interleaves latent visual spans with text in MLLM decoding, trained on a custom Future-L1-50K dataset via LA-DAPO RL, and reports SOTA gains on FutureBench (61.0 to 85.4) and TwiFF-Bench (2.44 to 3.04).
LoopMoE is a looped MoE language model that outperforms matched vanilla MoE on 8 of 9 downstream benchmarks at 3B scale and continues to outperform at 9B scale under strictly controlled budgets.
DeepLatent introduces a parallel latent visual reasoning framework with learnable 2D tokens and continuous RL, trained via distillation then RL, plus a new 180K dataset, claiming SOTA benchmark results.
RiM trains LLMs to perform latent reasoning via fixed memory blocks processed in one forward pass using a two-stage curriculum, matching or exceeding prior latent methods on benchmarks.
PlanAudio introduces a unified autoregressive LLM framework with semantic latent chain-of-thought for generating composite speech and sound audio from free-form text, plus a new benchmark.
STORM teaches LVLMs to internalize spatial-temporal reasoning via bounded latent trajectories trained with generated thought videos in two stages, improving accuracy on VideoMME, MVBench and similar benchmarks while lowering inference overhead.
SLT selectively compresses reasoning spans via anticipation and gating, trained in three stages including RL, yielding 22.7% higher accuracy than uniform latent baselines at similar compression and 58.4% shorter chains with 2.8% accuracy drop vs explicit CoT on math benchmarks.
Training-free looped transformers retrofit recurrence to frozen models via damped ODE sub-steps on mid-stack blocks, yielding gains such as +2.64 pp on MMLU-Pro for Qwen3-4B.
Self-Policy Distillation extracts a capability subspace from model gradients on correctness tokens, projects KV activations into it for self-generation, and fine-tunes LLMs to achieve up to 13-16% gains over baselines without external signals.
LatentOmni proposes a latent-space cross-modal reasoning framework that uses feature-level supervision and Omni-Sync Position Embedding to align and synchronize audio-visual latents, supported by a new 35K interleaved reasoning dataset and showing gains over text CoT baselines.
CopT reverses CoT by eliciting a draft answer first then using continuous-embedding contrastive verification and on-policy thinking to reflect and correct, yielding up to 23% higher accuracy and 57% fewer tokens without training.
PluRule is a new multimodal multilingual benchmark showing that state-of-the-art vision-language models perform only marginally better than a trivial baseline at detecting specific rule violations in pluralistic online communities.
ATLAS uses a single functional token to unify agentic and latent visual reasoning without image generation or external execution.
citing papers explorer
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Rethinking the Role of Positional Encoding: Sliding-Window Transformers without PE Remain Turing Complete
Sliding-window transformers without positional encodings are Turing complete because the sliding window breaks permutation symmetry and suffices to simulate Post machines via a constant-size histogram state.
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Transformers Provably Learn to Internalize Chain-of-Thought
L-layer transformers under Log-ICoT curriculum provably learn k-parity with poly(n) samples and log k stages, matching explicit CoT efficiency without inference overhead.
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A First-Principles Theory of Slow Thinking and Active Perception
Active lifting of data distributions via latent-sequence sampling and max-rate uncertainty reduction formally derives slow-thinking LLMs and places them on representation and sampler hierarchies that can be climbed.
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DiscoLoop: Looping Discrete Embeddings and Continuous Hidden States for Multi-hop Reasoning
DiscoLoop adds a decoded token-embedding channel to looped transformers, fixing a representation mismatch that limited implicit multi-hop reasoning and improving OOD generalization.
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Does Verbose Chain-of-Thought Really Help? In-Distribution Evidence that Content, Not Length, Matters
In-distribution sampling across 25 models and controlled interventions with DAG-verified content show that semantic reasoning and validation content, not token count, drive CoT gains.
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Efficient and Trainable Language Model Test-Time Scaling via Local Branch Routing
LBR performs token-level test-time scaling via local branch routing on hidden states, enabling end-to-end RL training and improving Pass@1 and Pass@32 on math benchmarks over CoT and RLVR baselines.
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Learning through Internalization
A simplified one-layer transformer provably learns parities first with explicit CoT supervision then internalizes to direct computation as CoT tokens are removed.
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PearlVLA: Progressive Embodied Action-Plan Refinement in Latent Space
PearlVLA achieves SOTA on LIBERO by separating VLM representations into visual grounding and an iterative latent plan branch refined via world model queries and RefineNet with process-reward RL.
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See What I See, Know What I Think: Dense Latent Communication Across Heterogeneous Agents
Heterogeneous agents achieve dense latent KV-cache communication via lightweight cross-model transformation and two-phase training, outperforming text at lower compute in context-aware settings and enabling context-unaware transfer.
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Demystifying Hidden-State Recurrence: Switchable Latent Reasoning with On-Policy Reinforcement Learning
SWITCH uses explicit <swi> and </swi> boundary tokens to make latent chain-of-thought compatible with on-policy RL (GRPO) and open to causal mechanistic probing, outperforming prior hidden-state recurrence methods.
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Beyond Matching: Category-Guided Latent Intent Reasoning for Generative Retrieval in E-Commerce
CaLIR learns continuous latent intent states guided by product category hierarchies for generative retrieval, combining hierarchical reasoning and dynamic prefix tries to balance effectiveness and low-latency inference on multilingual e-commerce data.
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Imagine Before You Predict: Interleaved Latent Visual Reasoning for Video Event Prediction
Future-L1 interleaves latent visual spans with text in MLLM decoding, trained on a custom Future-L1-50K dataset via LA-DAPO RL, and reports SOTA gains on FutureBench (61.0 to 85.4) and TwiFF-Bench (2.44 to 3.04).
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LoopMoE: Unifying Iterative Computation with Mixture-of-Experts for Language Modeling
LoopMoE is a looped MoE language model that outperforms matched vanilla MoE on 8 of 9 downstream benchmarks at 3B scale and continues to outperform at 9B scale under strictly controlled budgets.
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DeepLatent: Think with Images via Parallel Latent Visual Reasoning
DeepLatent introduces a parallel latent visual reasoning framework with learnable 2D tokens and continuous RL, trained via distillation then RL, plus a new 180K dataset, claiming SOTA benchmark results.
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Unlocking the Working Memory of Large Language Models for Latent Reasoning
RiM trains LLMs to perform latent reasoning via fixed memory blocks processed in one forward pass using a two-stage curriculum, matching or exceeding prior latent methods on benchmarks.
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Unified Synthesis of Compositional Speech and Sound from Free-Form Text Prompts
PlanAudio introduces a unified autoregressive LLM framework with semantic latent chain-of-thought for generating composite speech and sound audio from free-form text, plus a new benchmark.
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STORM: Internalized Modeling for Spatial-Temporal Reasoning in Video-Language Models
STORM teaches LVLMs to internalize spatial-temporal reasoning via bounded latent trajectories trained with generated thought videos in two stages, improving accuracy on VideoMME, MVBench and similar benchmarks while lowering inference overhead.
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Selective Latent Thinking: Adaptive Compression of LLM Reasoning Chains
SLT selectively compresses reasoning spans via anticipation and gating, trained in three stages including RL, yielding 22.7% higher accuracy than uniform latent baselines at similar compression and 58.4% shorter chains with 2.8% accuracy drop vs explicit CoT on math benchmarks.
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Training-Free Looped Transformers
Training-free looped transformers retrofit recurrence to frozen models via damped ODE sub-steps on mid-stack blocks, yielding gains such as +2.64 pp on MMLU-Pro for Qwen3-4B.
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Self-Policy Distillation via Capability-Selective Subspace Projection
Self-Policy Distillation extracts a capability subspace from model gradients on correctness tokens, projects KV activations into it for self-generation, and fine-tunes LLMs to achieve up to 13-16% gains over baselines without external signals.
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LatentOmni: Rethinking Omni-Modal Understanding via Unified Audio-Visual Latent Reasoning
LatentOmni proposes a latent-space cross-modal reasoning framework that uses feature-level supervision and Omni-Sync Position Embedding to align and synchronize audio-visual latents, supported by a new 35K interleaved reasoning dataset and showing gains over text CoT baselines.
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CopT: Contrastive On-Policy Thinking with Continuous Spaces for General and Agentic Reasoning
CopT reverses CoT by eliciting a draft answer first then using continuous-embedding contrastive verification and on-policy thinking to reflect and correct, yielding up to 23% higher accuracy and 57% fewer tokens without training.
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PluRule: A Benchmark for Moderating Pluralistic Communities on Social Media
PluRule is a new multimodal multilingual benchmark showing that state-of-the-art vision-language models perform only marginally better than a trivial baseline at detecting specific rule violations in pluralistic online communities.
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ATLAS: Agentic or Latent Visual Reasoning? One Word is Enough for Both
ATLAS uses a single functional token to unify agentic and latent visual reasoning without image generation or external execution.
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UniVLR: Unifying Text and Vision in Visual Latent Reasoning for Multimodal LLMs
UniVLR unifies textual and visual reasoning in multimodal LLMs by compressing reasoning traces and auxiliary images into visual latent tokens for direct inference without interleaved text CoT.
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Post Reasoning: Improving the Performance of Non-Thinking Models at No Cost
Post-Reasoning boosts LLM accuracy by reversing the usual answer-after-reasoning order, delivering mean relative gains of 17.37% across 117 model-benchmark pairs with zero extra cost.
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4DThinker: Thinking with 4D Imagery for Dynamic Spatial Understanding
4DThinker enables VLMs to perform dynamic spatial reasoning by thinking with 4D latent mental imagery using new fine-tuning and reinforcement learning methods.
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Latent State Design for World Models under Sufficiency Constraints
World models succeed when their latent states are built to meet task-specific sufficiency constraints rather than preserving the maximum amount of information.
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Semantic Step Prediction: Multi-Step Latent Forecasting in LLM Reasoning Trajectories via Step Sampling
Applying STP at consecutive semantic reasoning steps achieves 168x more accurate multi-step latent prediction on ProcessBench than frozen baselines, with trajectories forming smooth curves best captured by non-linear predictors.
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Latent Abstraction for Retrieval-Augmented Generation
LAnR unifies retrieval-augmented generation inside a single LLM by deriving dense retrieval vectors from a [PRED] token's hidden states and using entropy to adaptively stop retrieval, outperforming prior RAG on six QA benchmarks with better efficiency.
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Learning 3D Reconstruction with Priors in Test Time
Test-time constrained optimization incorporates priors into pre-trained multiview transformers via self-supervised losses and penalty terms to improve 3D reconstruction accuracy.
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PLUME: Latent Reasoning Based Universal Multimodal Embedding
PLUME uses latent-state autoregressive rollouts and a progressive training curriculum to deliver efficient reasoning for universal multimodal embeddings without generating explicit rationales.
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V-Reflection: Transforming MLLMs from Passive Observers to Active Interrogators
V-Reflection introduces a think-then-look mechanism where MLLM latent states actively interrogate visual features via two-stage distillation from a box-guided teacher to a dynamic autoregressive student, narrowing the fine-grained perception gap on benchmarks.
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The Silent Thought: Modeling Internal Cognition in Full-Duplex Spoken Dialogue Models via Latent Reasoning
Causal full-duplex speech LLMs improve response quality by recursively feeding soft vocabulary embeddings as latent thoughts during listening, trained by matching a non-causal expert posterior via ELBO.
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Reasoning over Video: Evaluating How MLLMs Extract, Integrate, and Reconstruct Spatiotemporal Evidence
VAEX-BENCH shows state-of-the-art MLLMs perform substantially worse on abstractive spatiotemporal reasoning tasks than on matched extractive tasks in video understanding.
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S$^2$GR: Stepwise Semantic-Guided Reasoning in Latent Space for Generative Recommendation
S²GR adds stepwise thinking tokens with contrastive supervision on codebook clusters to balance computational focus and ground reasoning paths in generative recommendation.
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Forest Before Trees: Latent Superposition for Efficient Visual Reasoning
Laser reformulates visual reasoning via Dynamic Windowed Alignment Learning to maintain latent superposition of global features, delivering 5.03% average gains over Monet and over 97% fewer inference tokens on six benchmarks.
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Reasoning Within the Mind: Dynamic Multimodal Interleaving in Latent Space
DMLR performs dynamic visual-textual interleaving in latent space using confidence-guided latent policy gradient optimization and a dynamic visual injection strategy, yielding improved multimodal reasoning on benchmarks.
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Latent Chain-of-Thought World Modeling for End-to-End Driving
LCDrive unifies chain-of-thought reasoning and action selection for end-to-end driving by interleaving action-proposal tokens and latent world-model tokens that predict action outcomes, yielding faster inference and better trajectories than text-based or non-reasoning baselines.
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Coevolutionary Continuous Discrete Diffusion: Make Your Diffusion Language Model a Latent Reasoner
CCDD defines a joint multimodal diffusion on continuous representation space and discrete token space to combine expressivity with explicit token supervision for diffusion language models.
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Latent Visual Reasoning
Latent Visual Reasoning enables autoregressive generation of latent visual states that reconstruct critical image tokens, yielding gains on perception-heavy VQA benchmarks such as 71.67% on MMVP.
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GRIT: Teaching MLLMs to Think with Images
GRIT introduces a grounded reasoning paradigm for MLLMs where reasoning chains interleave text and bounding boxes, trained via GRPO-GR reinforcement learning on as few as 20 examples without annotations.
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CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation
CODI compresses explicit CoT into continuous space via self-distillation and is the first implicit method to match explicit CoT performance on GSM8k at GPT-2 scale with 3.1x compression and 28.2% higher accuracy than prior implicit approaches.
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Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach
A recurrent-depth architecture enables language models to improve reasoning performance by iterating computation in latent space, achieving gains equivalent to much larger models on benchmarks.
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Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs
o1-like models overthink easy tasks; self-training reduces compute use without accuracy loss on GSM8K, MATH500, GPQA, and AIME.
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Final Checkpoints Are Not Enough: Analyzing Latent Reasoning Faithfulness Along Training Trajectories
Latent reasoning faithfulness is a property of training stage and answer format, not of architecture or the final checkpoint alone.
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Multimodal Continuous Reasoning via Asymmetric Mutual Variational Learning
AMVL applies bidirectional KL calibration to align answer-agnostic prior with answer-conditioned posterior in variational multimodal reasoning, reducing leakage and yielding +10.83 average gain on BLINK benchmark.
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CoLT: Teaching Multi-Modal Models to Think with Chain of Latent Thoughts
CoLT replaces text chain-of-thought in multimodal LLMs with three supervised latent vectors, improving average accuracy from 75.7 to 79.1 across eight benchmarks while cutting text-decoding time 22.6x.
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VisReflect: Latent Visual Reflection for Fine-Grained Perception in Long Visual Context
VisReflect generates continuous latent visual reflections to emphasize relevant visual features and guide attention in LVLMs, yielding 4.1% gains on image benchmarks and 1.8% on video benchmarks with 44% less inference time than zooming methods.
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Latent Noise Mask for Reducing Visual Redundancy in Multimodal Large Language Models
Lens purifies visual evidence in MLLMs via question-conditioned latent noise masking with a LET token, yielding 2.4-6.4 point gains on VQA and grounding tasks.