Awesome Loop Models

Models that compute by looping: one learned layer, block, or operator, reused across depth or folded into time.

🌐 Interactive Browser · 🧾 PR Submission Guide

_{The full catalog lives in the browser: search, browse by chapter, filter by section and loop design, and read TL;DRs, venues, code links, and daily briefings.}

News

• 2026-07-17 — The browser gained a Release Intelligence view: publication pulse, long-term trends, and dossiers for the latest releases. Explore stats
• 2026-04-24 — Awesome Loop Models is released. Announcement

What is a loop model?

A shared learned layer, block, module, or operator is reused, either along depth within one forward pass or along time, by feeding a state it computed back through the same layers for the next token or step.

That covers looped, recurrent-depth, and weight-tied Transformers, adaptive halting over a reused block, deep-equilibrium and implicit layers, shared neural algorithmic processors, and models that fold depth into time by feeding high-level states back through the same layers (Feedback Transformers, Latent Recurrent Transformers, shift-1 loops), plus theory and analysis of all of these. It leaves out agent loops, repeated full-model calls, diffusion-style iterative inference, and ordinary sequence recurrence that only carries a memory across steps. TAXONOMY.md has the full rules.

Where the scope boundary sits

Only the rightmost end of this scale is in scope. Omitting catalog_fit means strict scope; the rare exceptions kept for context set catalog_fit: adjacent and are labeled Adjacent work.

How the catalog is organized

The catalog is organized as a topic map of chapters and sections. Each paper lists every section it belongs to, primary first, and the browser files it under that primary section.

Part	Chapters
I. Foundations	§2 From recurrent computation to iterative depth
II. What looping buys	§3 Capabilities, benefits and trade-offs
III. Building, training and deploying	§4 Architecture · §5 Learning algorithms · §6 Scaling laws · §7 Systems
IV. Understanding and applications	§8 Why looped models work · §9 Applications
V. Open problems	§10 Diffusion · folding depth into time · monitorability and safety

Every paper also records its design axes (loop_topology, sharing, depth_control) and what it claims looping buys (claims, comparison). All values are controlled; there are no free-form tags. Blogs sit in one flat section and list only the sections they discuss. TAXONOMY.md explains each value and TAGS.md shows current counts.

At a glance

373 papers · 32 sections · 8 blogs · browse all →

🗺️ Topic map

The catalog is organized into chapters and sections. A paper is counted once under its primary section and again under every other section it belongs to.

Papers per section

§	Section	Primary	Any
§2.1	From Recurrent Computation to Iterative Depth › Recurrent networks and weight sharing across computation	2	3
§2.2	From Recurrent Computation to Iterative Depth › Weight sharing across network depth	4	6
§2.3	From Recurrent Computation to Iterative Depth › Deep equilibrium and implicit models	7	11
§2.4	From Recurrent Computation to Iterative Depth › Iterative and algorithmic computation	4	8
§3.1	Capabilities, Benefits and Trade-offs › Parameter, data, and compute efficiency	7	47
§3.2	Capabilities, Benefits and Trade-offs › Expressivity and reasoning capacity	19	23
§3.3	Capabilities, Benefits and Trade-offs › Length, easy-to-hard, and compositional generalization	12	24
§4.1	Architecture and Design › Loop topology	13	30
§4.2	Architecture and Design › Residual manipulation and initialization	9	37
§4.3	Architecture and Design › Recurrent state and loop-time memory	10	25
§4.4	Architecture and Design › Weight-sharing schemes and iteration-dependent computation	6	28
§4.5	Architecture and Design › Controlling recurrence depth	22	68
§4.6	Architecture and Design › Hybrid looped architectures	19	28
§5.1	Learning Algorithms › Supervision, credit assignment, and loop-specific optimization	25	74
§5.2	Learning Algorithms › Post-training and reinforcement learning	8	16
§5.3	Learning Algorithms › Retrofitting pretrained models into looped models	14	24
§6.1	Scaling Laws › Parameter, depth, and compute-optimal scaling	8	19
§6.2	Scaling Laws › Test-time scaling	12	49
§7.1	Systems and Infrastructure › Quantization and edge deployment	10	15
§7.2	Systems and Infrastructure › KV cache and memory	11	20
§7.3	Systems and Infrastructure › Loop-level batching, scheduling, and parallel execution	7	12
§8.1	Understanding Why Looped Models Work › Why looped models work	3	16
§8.2	Understanding Why Looped Models Work › Mechanistic interpretability	24	37
§8.3	Understanding Why Looped Models Work › When looping does not help: limits and failure modes	12	39
§9.1	Applications › Language, code, speech, and multimodal tasks	29	37
§9.2	Applications › Visual recognition, restoration, and generation	23	31
§9.3	Applications › Flow, stereo, and 3D geometry	5	5
§9.4	Applications › Graphs, structured data, and scientific modeling	19	29
§9.5	Applications › Embodied AI and other domains	24	27
§10.1	Open Problems › Unification with diffusion models	3	12
§10.2	Open Problems › Folding depth into time	1	6
§10.3	Open Problems › Monitorability and safety	1	4

🌟 Start here

Core references for loop models, plus the ones the maintainer marks as must-read.

Paper	Venue	Loop	Links
Deeply-Recursive Convolutional Network for Image Super-Resolution	CVPR 2016	prelude-core-coda	arXiv
Adaptive Computation Time for Recurrent Neural Networks	2016	whole-stack	arXiv
Universal Transformers	ICLR 2019	whole-stack	arXiv · Code ★17,472
Deep Equilibrium Models	NeurIPS 2019	implicit-fixed-point	arXiv · Code ★813
ALBERT: A Lite BERT for Self-supervised Learning of Language Representations	ICLR 2020	whole-stack	arXiv · Code ★3,276
Neural Execution of Graph Algorithms	ICLR 2020	prelude-core-coda	arXiv
RAFT: Recurrent All-Pairs Field Transforms for Optical Flow	ECCV 2020	partial	arXiv · Code ★4,119
Monotone operator equilibrium networks	NeurIPS 2020	implicit-fixed-point	arXiv · Code ★54
Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks	NeurIPS 2021	prelude-core-coda	arXiv · Code ★61
PonderNet: Learning to Ponder	AutoML Workshop @ ICML 2021	whole-stack	arXiv
End-to-end Algorithm Synthesis with Recurrent Networks: Extrapolation without Overthinking	NeurIPS 2022	prelude-core-coda	arXiv · Code ★92
Path Independent Equilibrium Models Can Better Exploit Test-Time Computation	NeurIPS 2022	implicit-fixed-point	arXiv
Looped Transformers as Programmable Computers	ICML 2023	whole-stack	arXiv
Looped Transformers are Better at Learning Learning Algorithms	ICLR 2024	whole-stack	arXiv · Code ★73
MoEUT: Mixture-of-Experts Universal Transformers	NeurIPS 2024	whole-stack	arXiv · Code ★93
Looped Transformers for Length Generalization	ICLR 2025	whole-stack	arXiv · Code ★15
Relaxed Recursive Transformers: Effective Parameter Sharing with Layer-wise LoRA	ICLR 2025	whole-stack	arXiv
🌟 Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach	NeurIPS 2025	prelude-core-coda	arXiv · Code ★989 · HF
Reasoning with Latent Thoughts: On the Power of Looped Transformers	ICLR 2025	whole-stack	arXiv
Hierarchical Reasoning Model	2025	hierarchical	arXiv · Code ★12,665
Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation	NeurIPS 2025	whole-stack	arXiv · Code ★648
Less is More: Recursive Reasoning with Tiny Networks	2025	hierarchical	arXiv · Code ★6,554
Parallel Loop Transformer for Efficient Test-Time Computation Scaling	2025	shifted-parallel	arXiv
🌟 Scaling Latent Reasoning via Looped Language Models	2025	whole-stack	arXiv · HF · Project
Teaching Pretrained Language Models to Think Deeper with Retrofitted Recurrence	2025	prelude-core-coda	arXiv · Code ★72 · HF
🌟 Parcae: Scaling Laws For Stable Looped Language Models	LIT Workshop @ ICLR 2026	prelude-core-coda	arXiv

🆕 Latest additions

Added	Paper	§	Links
2026-10-29	Depth through Recurrence: Towards Ultra-Efficient On-Device ASR	§9.1	arXiv
2026-10-29	Think Twice: The Metis-1.6 Technical Report	§4.6	arXiv · HF
2026-10-29	Tiny Recursive Policy: Recursive Latent Refinement for Visuomotor Control	§9.5	arXiv
2026-10-29	Multiclass Boundary Refinement with Neural Cellular Automata for Remote Sensing Land Cover Segmentation	§9.2	arXiv
2026-10-27	LoopFold: Parallelizing Recurrent Depth in Looped Transformers	§7.3	arXiv
2026-10-27	StateLoop: Persistent State for Looped Transformers	§4.3	arXiv
2026-10-27	Cross-Loop Query Handoff: How Later Loops Redirect Two-Hop Retrieval in the Ouro Looped Language Models	§8.2	arXiv · Code ★1
2026-10-27	LoopGR: Parameter-Efficient Scaling for Generative Recommendation via Recurrent Depth	§9.5	arXiv
2026-10-27	Prefix Keys and Values Matter Late: RIPE Caching for Self-Speculative Decoding in Looped Language Models	§7.2	arXiv
2026-10-27	Recursive CLIP: Vision-Language Distillation with Looped Transformer Blocks	§9.1	arXiv

_{A daily watch adds new arXiv papers. The browser has every paper and each day's briefing.}

🔥 Most cited

Paper	Venue	Citations	Links
ALBERT: A Lite BERT for Self-supervised Learning of Language Representations	ICLR 2020	7,881	arXiv · Code ★3,276
RAFT: Recurrent All-Pairs Field Transforms for Optical Flow	ECCV 2020	4,433	arXiv · Code ★4,119
Deeply-Recursive Convolutional Network for Image Super-Resolution	CVPR 2016	3,128	arXiv
Universal Transformers	ICLR 2019	1,175	arXiv · Code ★17,472
Deep Equilibrium Models	NeurIPS 2019	1,074	arXiv · Code ★813
Adaptive Computation Time for Recurrent Neural Networks	2016	951	arXiv
🌟 Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach	NeurIPS 2025	520	arXiv · Code ★989 · HF
Neural GPUs Learn Algorithms	ICLR 2016	412	arXiv · Code ★145
Looped Transformers as Programmable Computers	ICML 2023	310	arXiv
Reasoning with Latent Thoughts: On the Power of Looped Transformers	ICLR 2025	304	arXiv

✍️ Blogs

Long-form technical posts on loop models.

Date	Post	Where	Links
2026-07-31	Towards Looped Models Done Right — Part I: Topology, Input Injection, Recurrent-State Design	IFM Research	Read
2026-05-23	Rethinking Hierarchy in Iterative Reasoning Models	X Article	Read
2026-04-29	Exact Input Writes Improve Stable Looped Language Models	Personal Blog	Read · Code
2026-04-21	Claude Mythos, Looped LLM, and the Depth Scaling Axis	X Article	Read
2026-04-19	Loop-Model FLOPs and Memory in an Ablation Chain	Personal Blog	Read
2026-04-19	On the Looped Transformers Controversy	X Article	Read
2026-01-12	Looped-GPT: Looping During Pre-training improves Generalization	Personal Blog	Read · Code
2020-01-07	Adaptive Computation Time (ACT) in Neural Networks [3/3]	Medium	Read

Contributing

Additions, corrections, and scope challenges are welcome. The PR Submission Guide turns a paper or blog into generated YAML; add that file to papers/ or blogs/ in a branch in your fork and open a pull request. See CONTRIBUTING.md, TAXONOMY.md, and TAGS.md.

Citation

@misc{huang2026awesomeloopmodels,
    title = {Awesome-Loop-Models},
    author = {Benhao Huang and {Awesome-Loop-Models Contributors}},
    journal = {GitHub repository},
    url = {https://github.com/huskydoge/Awesome-Loop-Models},
    year = {2026},
}

Star History

_{Maintained by huskydoge · generated from papers/*.yaml and blogs/*.yaml by scripts/build.py}