Awesome Loop Models
Models that compute by looping: one learned layer, block, or operator, reused inside a single forward pass.
🌐 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?
Within a single forward pass, a shared learned layer, block, module, or operator is reused.
That covers looped, recurrent-depth, and weight-tied Transformers, adaptive halting over a reused block, deep-equilibrium and implicit layers, and shared neural algorithmic processors, plus theory and analysis of all of these. It leaves out agent loops, repeated full-model calls, diffusion-style iterative inference, and plain recurrence over time 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
333 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 | 38 | | §3.2 | Capabilities, Benefits and Trade-offs › Expressivity and reasoning capacity | 18 | 22 | | §3.3 | Capabilities, Benefits and Trade-offs › Length, easy-to-hard, and compositional generalization | 10 | 22 | | §4.1 | Architecture and Design › Loop topology | 10 | 25 | | §4.2 | Architecture and Design › Residual manipulation and initialization | 9 | 32 | | §4.3 | Architecture and Design › Recurrent state and loop-time memory | 8 | 17 | | §4.4 | Architecture and Design › Weight-sharing schemes and iteration-dependent computation | 6 | 25 | | §4.5 | Architecture and Design › Controlling recurrence depth | 19 | 59 | | §4.6 | Architecture and Design › Hybrid looped architectures | 18 | 24 | | §5.1 | Learning Algorithms › Supervision, credit assignment, and loop-specific optimization | 24 | 67 | | §5.2 | Learning Algorithms › Post-training and reinforcement learning | 7 | 14 | | §5.3 | Learning Algorithms › Retrofitting pretrained models into looped models | 12 | 19 | | §6.1 | Scaling Laws › Parameter, depth, and compute-optimal scaling | 7 | 17 | | §6.2 | Scaling Laws › Test-time scaling | 12 | 47 | | §7.1 | Systems and Infrastructure › Quantization and edge deployment | 10 | 14 | | §7.2 | Systems and Infrastructure › KV cache and memory | 8 | 17 | | §7.3 | Systems and Infrastructure › Loop-level batching, scheduling, and parallel execution | 6 | 9 | | §8.1 | Understanding Why Looped Models Work › Why looped models work | 1 | 12 | | §8.2 | Understanding Why Looped Models Work › Mechanistic interpretability | 21 | 32 | | §8.3 | Understanding Why Looped Models Work › When looping does not help: limits and failure modes | 11 | 37 | | §9.1 | Applications › Language, code, speech, and multimodal tasks | 25 | 33 | | §9.2 | Applications › Visual recognition, restoration, and generation | 20 | 28 | | §9.3 | Applications › Flow, stereo, and 3D geometry | 5 | 5 | | §9.4 | Applications › Graphs, structured data, and scientific modeling | 18 | 27 | | §9.5 | Applications › Embodied AI and other domains | 20 | 23 | | §10.1 | Open Problems › Unification with diffusion models | 2 | 11 | | §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 | | Deep Equilibrium Models | NeurIPS 2019 | implicit-fixed-point | arXiv · Code ★811 | | 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 ★4,116 | | 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 ★71 | | MoEUT: Mixture-of-Experts Universal Transformers | NeurIPS 2024 | whole-stack | arXiv · Code ★93 | | Looped Transformers for Length Generalization | ICLR 2025 | whole-stack | arXiv · Code ★14 | | 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 ★983 · HF | | Reasoning with Latent Thoughts: On the Power of Looped Transformers | ICLR 2025 | whole-stack | arXiv | | Hierarchical Reasoning Model | 2025 | hierarchical | arXiv · Code ★12,658 | | Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation | NeurIPS 2025 | whole-stack | arXiv · Code ★642 | | Less is More: Recursive Reasoning with Tiny Networks | 2025 | hierarchical | arXiv · Code ★6,556 | | 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 ★71 · HF | | 🌟 Parcae: Scaling Laws For Stable Looped Language Models | LIT Workshop @ ICLR 2026 | prelude-core-coda | arXiv |
🆕 Latest additions
| Added | Paper | § | Links | |:--|:--|:--|:--| | 2026-10-18 | AdaLoop: Thinking with the Vision Encoder | §9.1 | arXiv | | 2026-10-18 | LoopAhead: Speculating Ahead for Faster Decoding in Looped Language Models | §7.3 | arXiv | | 2026-10-18 | Retrofitting Recurrent Vision-Language Models from Pretrained Backbones | §5.3 | arXiv · Project | | 2026-10-18 | LEV: Thinking Fast and Deep with Looped Decision Models | §4.5 | arXiv · Code ★3 · HF · Project | | 2026-10-18 | Trading Depth for Time in Recurrent Transformers | §10.2 | arXiv · Code | | 2026-10-15 | LatentLoop: Scaling Looped MoE Models with Asymmetric Compute Allocation | §4.6 | arXiv · Code ★11 · Project | | 2026-10-15 | Learning to Compute Is Not Learning to Retain or Reuse in Looped Transformers | §8.3 | arXiv | | 2026-10-15 | Test-Time Forecasting: Recurrent Depth Enables In-Context Dynamics Prediction | §3.2 | arXiv | | 2026-10-15 | Riding the Fixed-Point Curve: Image Classification in the Continuous Thought Machine | §8.1 | arXiv | | 2026-10-15 | Diffusion as a Training Curriculum for Timestep-Free Iterative Reasoning | §5.1 | 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 | 7,800 | arXiv · Code ★3,276 | | RAFT: Recurrent All-Pairs Field Transforms for Optical Flow | ECCV 2020 | 4,334 | arXiv · Code ★4,116 | | Deeply-Recursive Convolutional Network for Image Super-Resolution | CVPR 2016 | 3,123 | arXiv | | Universal Transformers | ICLR 2019 | 1,138 | arXiv | | Deep Equilibrium Models | NeurIPS 2019 | 1,042 | arXiv · Code ★811 | | Adaptive Computation Time for Recurrent Neural Networks | 2016 | 923 | arXiv | | 🌟 Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach | NeurIPS 2025 | 473 | arXiv · Code ★983 · HF | | Neural GPUs Learn Algorithms | ICLR 2016 | 411 | arXiv · Code ★144 | | Looped Transformers as Programmable Computers | ICML 2023 | 288 | arXiv | | Reasoning with Latent Thoughts: On the Power of Looped Transformers | ICLR 2025 | 279 | 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