Looped transformers with recall and outer normalization produce reachable, input-dependent fixed points with stable gradients, enabling generalization, while those without recall cannot; a new internal recall variant performs competitively or better.
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Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach
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We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This stands in contrast to mainstream reasoning models that scale up compute by producing more tokens. Unlike approaches based on chain-of-thought, our approach does not require any specialized training data, can work with small context windows, and can capture types of reasoning that are not easily represented in words. We scale a proof-of-concept model to 3.5 billion parameters and 800 billion tokens. We show that the resulting model can improve its performance on reasoning benchmarks, sometimes dramatically, up to a computation load equivalent to 50 billion parameters.
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CanViT is the first task- and policy-agnostic AVFM pretrained via passive-to-active dense latent distillation on 13.2M scenes and 1B random glimpses, achieving 38.5% ADE20K mIoU in one glimpse and 84.5% ImageNet-1k top-1 after fine-tuning.
Flow models reach 99.2% Sudoku accuracy in 7 passes and 96.1% on out-of-distribution Sudoku-Extreme by selecting dynamically stable candidates and training with self-conditioning plus DPO to avoid failed outputs.
Recursive Masked Diffusion Models add recursive depth via repeated application of the same transformer to improve parameter efficiency and reduce inference steps in masked diffusion models.
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.
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.
Fully Looped Transformer stabilizes looped training up to 12 iterations via distributed inter-loop signals and attention injection, improving downstream performance by up to 13.2%.
Scratchpad Patching decouples compute from patch size in byte-level language models by inserting entropy-triggered scratchpads to update patch context dynamically.
LoopUS converts pretrained LLMs into looped latent refinement models via block decomposition, selective gating, random deep supervision, and confidence-based early exiting to improve reasoning performance.
Bifurcation models represent set-valued solution maps via weight-tied equilibrium dynamics whose attractors encode multiple solutions, with a proof that broad locally Lipschitz set-valued maps admit regular dynamical representations and experiments showing label-free discovery of multiple equilibria
Multi-layer transformers can implement in-context logistic regression by performing normalized gradient descent steps layer by layer, obtained via supervised training of a single attention layer followed by recurrent application with convergence and OOD guarantees.
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.
Looped LLMs converge to distinct cyclic fixed points per layer, repeating feedforward-style inference stages across recurrences.
LA-Sign achieves state-of-the-art skeleton-based sign language recognition on WLASL and MSASL by using recurrent looped transformers with adaptive hyperbolic geometry alignment.
Coconut lets LLMs perform reasoning directly in continuous latent space by recycling hidden states as inputs, outperforming standard chain-of-thought on search-intensive logical tasks with better accuracy-efficiency trade-offs.
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.
A looped padded Transformer with parallel gold-CoT cross-entropy supervision matches explicit CoT accuracy at 3B scale and is 2.5–6.9× faster in the thought phase.
Stochastic loop counts during training of looped transformers reduce OOD variance on binary addition, Dyck-1, Unique Set and Copy tasks, with learned RL-Halting further improving the accuracy-stability trade-off.
Context-ready transformer adds a correction network to pre-contextualize tokens in a D-layer block, turning the model recurrent for inference while allowing K-step unrolled parallel training, with reported gains over standard transformers.
A 2x2 ablation shows repeated shared access enables grokking while addressable memory (not recurrence) enables edit propagation in transformer variants on synthetic KG QA.
Introduces looped transformer architectures for world models that iteratively refine latent states to achieve up to 100x parameter efficiency via adaptive computation depth.
Dual-path blocks with deep shared and wide non-shared sublayers plus per-token gates outperform iso-FLOP baselines on language modeling while using fewer parameters.
LoopMDM loops early-middle layers in masked diffusion models to match same-size MDM performance with up to 3.3x fewer training FLOPs and outperform on reasoning tasks by up to 8.5 points on GSM8K.
GRAM is a latent-variable generative model that performs recursive reasoning via stochastic trajectories, trained with amortized variational inference to support multi-hypothesis reasoning and unconditional generation.
citing papers explorer
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Stability and Generalization in Looped Transformers
Looped transformers with recall and outer normalization produce reachable, input-dependent fixed points with stable gradients, enabling generalization, while those without recall cannot; a new internal recall variant performs competitively or better.
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CanViT: Toward Active-Vision Foundation Models
CanViT is the first task- and policy-agnostic AVFM pretrained via passive-to-active dense latent distillation on 13.2M scenes and 1B random glimpses, achieving 38.5% ADE20K mIoU in one glimpse and 84.5% ImageNet-1k top-1 after fine-tuning.
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Flow Reasoning Models: Scaling Reasoning Through Iterative Self-Refinement
Flow models reach 99.2% Sudoku accuracy in 7 passes and 96.1% on out-of-distribution Sudoku-Extreme by selecting dynamically stable candidates and training with self-conditioning plus DPO to avoid failed outputs.
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Recursive Scaling in Masked Diffusion Models
Recursive Masked Diffusion Models add recursive depth via repeated application of the same transformer to improve parameter efficiency and reduce inference steps in masked diffusion models.
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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.
-
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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Simply Stabilizing the Loop via Fully Looped Transformer
Fully Looped Transformer stabilizes looped training up to 12 iterations via distributed inter-loop signals and attention injection, improving downstream performance by up to 13.2%.
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Scratchpad Patching: Decoupling Compute from Patch Size in Byte-Level Language Models
Scratchpad Patching decouples compute from patch size in byte-level language models by inserting entropy-triggered scratchpads to update patch context dynamically.
-
LoopUS: Recasting Pretrained LLMs into Looped Latent Refinement Models
LoopUS converts pretrained LLMs into looped latent refinement models via block decomposition, selective gating, random deep supervision, and confidence-based early exiting to improve reasoning performance.
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Bifurcation Models: Learning Set-Valued Solution Maps with Weight-Tied Dynamics
Bifurcation models represent set-valued solution maps via weight-tied equilibrium dynamics whose attractors encode multiple solutions, with a proof that broad locally Lipschitz set-valued maps admit regular dynamical representations and experiments showing label-free discovery of multiple equilibria
-
Transformers Efficiently Perform In-Context Logistic Regression via Normalized Gradient Descent
Multi-layer transformers can implement in-context logistic regression by performing normalized gradient descent steps layer by layer, obtained via supervised training of a single attention layer followed by recurrent application with convergence and OOD guarantees.
-
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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A Mechanistic Analysis of Looped Reasoning Language Models
Looped LLMs converge to distinct cyclic fixed points per layer, repeating feedforward-style inference stages across recurrences.
-
LA-Sign: Looped Transformers with Geometry-aware Alignment for Skeleton-based Sign Language Recognition
LA-Sign achieves state-of-the-art skeleton-based sign language recognition on WLASL and MSASL by using recurrent looped transformers with adaptive hyperbolic geometry alignment.
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Training Large Language Models to Reason in a Continuous Latent Space
Coconut lets LLMs perform reasoning directly in continuous latent space by recycling hidden states as inputs, outperforming standard chain-of-thought on search-intensive logical tasks with better accuracy-efficiency trade-offs.
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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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Bridging the Gap Between Latent and Explicit Reasoning with Looped Transformers
A looped padded Transformer with parallel gold-CoT cross-entropy supervision matches explicit CoT accuracy at 3B scale and is 2.5–6.9× faster in the thought phase.
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Stabilizing Extrapolation in Looped Transformers via Learned Stochastic Stopping
Stochastic loop counts during training of looped transformers reduce OOD variance on binary addition, Dyck-1, Unique Set and Copy tasks, with learned RL-Halting further improving the accuracy-stability trade-off.
-
The Context-Ready Transformer
Context-ready transformer adds a correction network to pre-contextualize tokens in a D-layer block, turning the model recurrent for inference while allowing K-step unrolled parallel training, with reported gains over standard transformers.
-
Repeated Shared Access Enables Grokking, but Edit Propagation Depends on an Addressable Memory
A 2x2 ablation shows repeated shared access enables grokking while addressable memory (not recurrence) enables edit propagation in transformer variants on synthetic KG QA.
-
Looped World Models
Introduces looped transformer architectures for world models that iteratively refine latent states to achieve up to 100x parameter efficiency via adaptive computation depth.
-
A Dual-Path Architecture for Scaling Compute and Capacity in LLMs
Dual-path blocks with deep shared and wide non-shared sublayers plus per-token gates outperform iso-FLOP baselines on language modeling while using fewer parameters.
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Looped Diffusion Language Models
LoopMDM loops early-middle layers in masked diffusion models to match same-size MDM performance with up to 3.3x fewer training FLOPs and outperform on reasoning tasks by up to 8.5 points on GSM8K.
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Generative Recursive Reasoning
GRAM is a latent-variable generative model that performs recursive reasoning via stochastic trajectories, trained with amortized variational inference to support multi-hypothesis reasoning and unconditional generation.
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TTE-Flash: Accelerating Reasoning-based Multimodal Representations via Think-Then-Embed Tokens
TTE-Flash trains latent think tokens with CoT generation loss and embedding tokens with contrastive loss to deliver high-performance multimodal representations without generating explicit reasoning at inference time.
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Ensemble Monitoring for AI Control: Diverse Signals Outweigh More Compute
Diverse ensembles of prompted and fine-tuned GPT-4.1-Mini monitors achieve 2.4x better detection of flawed code solutions than homogeneous ensembles on adversarial inputs.
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Self-Consistent Latent Reasoning: Long Latent Sequence Reasoning for Vision-Language Model
SCOLAR fixes information gain collapse in latent visual reasoning by generating independent auxiliary visual tokens via a detransformer, extending acceptable CoT length over 30x and delivering +14.12% gains on reasoning benchmarks.
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Block-Based Double Decoders
Block-based double decoders use doubly-causal block attention masks to combine decoder-only training efficiency with encoder-decoder inference efficiency, outperforming standard encoder-decoders in scaling experiments.
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Memory-Efficient Looped Transformer: Decoupling Compute from Memory in Looped Language Models
MELT decouples reasoning depth from memory in looped language models by sharing a single gated KV cache per layer and training it via chunk-wise distillation from Ouro starting models.
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Factorized Latent Reasoning for LLM-based Recommendation
FLR factorizes latent reasoning into multiple preference factors using multi-factor attention and regularizations, outperforming baselines on recommendation benchmarks while adding robustness and interpretability.
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The Thinking Pixel: Recursive Sparse Reasoning in Multimodal Diffusion Latents
A recursive sparse MoE framework integrated into diffusion models iteratively refines visual tokens via gated module selection to improve structured reasoning and image generation performance.
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Universal Transformers Need Memory: Depth-State Trade-offs in Adaptive Recursive Reasoning
Memory tokens are required for non-trivial performance in adaptive Universal Transformers on Sudoku-Extreme, with 8-32 tokens yielding stable 57% exact-match accuracy while trading off against ponder depth.
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One Step Forward and K Steps Back: Better Reasoning with Denoising Recursion Models
Denoising Recursion Models train multi-step noise reversal in looped transformers and outperform the prior Tiny Recursion Model on ARC-AGI.
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C-voting: Confidence-Based Test-Time Voting without Explicit Energy Functions
C-voting improves recurrent reasoning models by selecting among multiple latent trajectories the one with highest average top-1 probability, achieving 4.9% better Sudoku-hard accuracy than energy-based voting and outperforming HRM on Sudoku-extreme and Maze when paired with the new ItrSA++ model.
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ELT: Elastic Looped Transformers for Visual Generation
Weight-shared looped transformers trained with intra-loop self-distillation match MaskGIT-class FID/FVD at roughly 4x fewer parameters and support any-time inference across loop counts.
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SeLaR: Selective Latent Reasoning in Large Language Models
SeLaR selectively applies latent soft reasoning in LLMs via entropy gating and contrastive regularization, outperforming standard CoT on five benchmarks without training.
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Representational Collapse in Multi-Agent LLM Committees: Measurement and Diversity-Aware Consensus
LLM agent committees exhibit representational collapse with mean cosine similarity of 0.888, and diversity-aware consensus reaches 87% accuracy on GSM8K versus 84% for self-consistency at lower cost.
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Mull-Tokens: Modality-Agnostic Latent Thinking
Mull-Tokens are modality-agnostic latent tokens that enable free-form multimodal thinking and deliver up to 16% gains on spatial reasoning benchmarks.
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Enabling Agents to Communicate Entirely in Latent Space
Exchanging LLM hidden states instead of text beats chain-of-thought communication in the paper's tests and can be compressed to 8 steps with a 24× speedup.
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A Unifying Framework for Parallelizing Sequential Models with Linear Dynamical Systems
A framework based on linear dynamical systems unifies fixed-point iteration schemes such as Newton, Picard, and Jacobi as approximate linearizations of nonlinear recursions for parallelizing sequential models.
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Dream 7B: Diffusion Large Language Models
Dream 7B is a 7B diffusion LLM that refines sequences in parallel via denoising and outperforms prior diffusion models on general, mathematical, and coding benchmarks with added flexibility in generation order and quality-speed tradeoffs.
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OpenVLThinker: Complex Vision-Language Reasoning via Iterative SFT-RL Cycles
Iterative SFT-RL cycles enable a 7B LVLM to develop sophisticated visual chain-of-thought reasoning and improve performance on math and general reasoning benchmarks.
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Dense Supervision Is Not Enough: The Readout Blind Spot in Looped Language Models
Dense per-loop cross-entropy in looped transformers fails to control hidden-state scale with scale-invariant readouts like RMSNorm, driving norms to thousands, while scale-visible readouts or norm penalties keep norms small and improve perplexity.
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Anti Mode-Collapse in Mean-Field Transformer via Auxiliary Variables
Auxiliary variables prevent mode collapse in mean-field transformers, with the limit distribution being the pushforward of the auxiliary distribution, and positional encoding and prompt insertion have universality of representation.
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Stabilizing Recurrent Dynamics for Test-Time Scalable Latent Reasoning in Looped Language Models
STARS trains looped language models with Jacobian spectral radius regularization and random loop sampling to drive latent states toward asymptotically stable fixed points, yielding reliable test-time scaling on arithmetic and mathematical reasoning tasks.
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Sparse Layers are Critical to Scaling Looped Language Models
Looped-MoE models scale better than dense looped or standard transformers because routing changes across loops, and they enable stronger compute-quality trade-offs via early exits at loop boundaries.
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SMolLM: Small Language Models Learn Small Molecular Grammar
A 53K-parameter weight-shared transformer generates novel valid SMILES at 95% rate on ZINC-250K and resolves constraints hierarchically via bracket, ring, and valence stages as shown by probing and ablation.
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Hyperloop Transformers
A looped Transformer with matrix-valued hyper-connections matches depth-matched baselines at ~50% fewer parameters, including under post-training quantization.
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HypEHR: Hyperbolic Modeling of Electronic Health Records for Efficient Question Answering
A 22M-parameter hyperbolic model answers structured EHR questions with accuracy close to LLM-based systems (EHRXQA 89.5%, MIMIC-Instr 76.0%).
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LEPO: Latent Reasoning Policy Optimization for Large Language Models
LEPO applies RL to continuous latent representations in LLMs by injecting Gumbel-Softmax stochasticity for diverse trajectory sampling and unified gradient estimation, outperforming existing discrete and latent RL methods.