# Hyperloop Transformers

arXiv: https://arxiv.org/abs/2604.21254 · HTML: https://mlsanity.com/paper/2604.21254/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 46 references that are in the map.
- First posted on arXiv 23 Apr 2026.

## Builds on (most cited first, 30 of 39)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [Looped Transformers as Programmable Computers](https://mlsanity.com/paper/2301.13196/) (2023)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [Looped Transformers are Better at Learning Learning Algorithms](https://mlsanity.com/paper/2311.12424/) (2023)
- [Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation](https://mlsanity.com/paper/2507.10524/) (2025)
- [The Devil is in the Detail: Simple Tricks Improve Systematic Generalization of Transformers](https://mlsanity.com/paper/2108.12284/) (2021)
- [Hyper-Connections](https://mlsanity.com/paper/2409.19606/) (2024)
- [Relaxed Recursive Transformers: Effective Parameter Sharing with Layer-wise LoRA](https://mlsanity.com/paper/2410.20672/) (2024)
- [An empirical study of LLaMA3 quantization: from LLMs to MLLMs](https://mlsanity.com/paper/2404.14047/) (2024)
- [The Neural Data Router: Adaptive Control Flow in Transformers Improves Systematic Generalization](https://mlsanity.com/paper/2110.07732/) (2021)
- [LoopFormer: Elastic-Depth Looped Transformers for Latent Reasoning via Shortcut Modulation](https://mlsanity.com/paper/2602.11451/) (2026)
- [MoEUT: Mixture-of-Experts Universal Transformers](https://mlsanity.com/paper/2405.16039/) (2024)
- [Parcae: Scaling Laws For Stable Looped Language Models](https://mlsanity.com/paper/2604.12946/) (2026)
- [DenseFormer: Enhancing Information Flow in Transformers via Depth Weighted Averaging](https://mlsanity.com/paper/2402.02622/) (2024)
- [Teaching Pretrained Language Models to Think Deeper with Retrofitted Recurrence](https://mlsanity.com/paper/2511.07384/) (2025)
- [Loop, Think, & Generalize: Implicit Reasoning in Recurrent-Depth Transformers](https://mlsanity.com/paper/2604.07822/) (2026)

## Built on by (most cited first, 12 of 12)

- [Solve the Loop: Attractor Models for Language and Reasoning](https://mlsanity.com/paper/2605.12466/) (2026)
- [LoopQ: Quantization for Looped Language Models](https://mlsanity.com/paper/2605.16343/) (2026)
- [Investigating Single-Block Recurrence in Vision Transformers for Image Recognition](https://mlsanity.com/paper/2605.10661/) (2026)
- [CART: Context-Anchored Recurrent Transformer -- A Parameter-Efficient Architecture with Learned Stability](https://mlsanity.com/paper/2606.01495/) (2026)
- [Tying the Loop -- Tied Expert Layers in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2606.16825/) (2026)
- [Looped World Models](https://mlsanity.com/paper/2606.18208/) (2026)
- [SNLP: Layer-Parallel Inference via Structured Newton Corrections](https://mlsanity.com/paper/2605.17842/) (2026)
- [Scaling Laws for Looped Mixture of Experts](https://mlsanity.com/paper/2609.40316/) (2026)
- [SMolLM: Small Language Models Learn Small Molecular Grammar](https://mlsanity.com/paper/2605.06322/) (2026)
- [Looped Transformers as Optimizers](https://mlsanity.com/paper/2609.37379/) (2026)
- [Universal interpolation for deep residual self-attention networks](https://mlsanity.com/paper/2610.01981/) (2026)
- [One Model to Loop Them All: Elastic Latent Recurrence for Language Models](https://mlsanity.com/paper/2610.12582/) (2026)

## Abstract (arXiv)

LLM architecture research generally aims to maximize model quality subject to fixed compute/latency budgets. However, many applications of interest such as edge and on-device deployment are further constrained by the model's memory footprint, thus motivating parameter-efficient architectures for language modeling. This paper describes a simple architecture that improves the parameter-efficiency of LLMs. Our architecture makes use of looped Transformers as a core primitive, which reuse Transformer layers across depth and are thus more parameter-efficient than ordinary (depth-matched) Transformers. We organize the looped Transformer into three blocks--begin, middle, and end blocks--where each block itself consists of multiple Transformer layers, and only the middle block is applied recurrently across depth. We augment the looped middle block with hyper-connections (Xie et al., 2026), which expand the residual stream into matrix-valued residual streams. Hyper-connections are applied only after each loop, and therefore add minimal new parameters and compute cost. Across various model scales, we find that our Hyper-Connected Looped Transformer (Hyperloop Transformer) is able to perform well compared to depth-matched Transformer and mHC Transformer baselines despite using approximately 50% fewer parameters. This performance persists through post-training weight quantization, thus positioning Hyperloop Transformers as an attractive architecture for memory-efficient language modeling.