# LoopMoE: Unifying Iterative Computation with Mixture-of-Experts for Language Modeling

arXiv: https://arxiv.org/abs/2606.04438 · HTML: https://mlsanity.com/paper/2606.04438/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in MoE large language models, one of 12 directions in Mixture-of-experts.
- Builds on 31 of its 49 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Placed in

- Mixture-of-experts / [MoE large language models](https://mlsanity.com/moe/moe-large-language-models/)

## Builds on (most cited first, 30 of 31)

- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [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)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models](https://mlsanity.com/paper/2508.06471/) (2025)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [OpenMoE: An Early Effort on Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2402.01739/) (2024)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation](https://mlsanity.com/paper/2507.10524/) (2025)
- [CoLT5: Faster Long-Range Transformers with Conditional Computation](https://mlsanity.com/paper/2303.09752/) (2023)
- [Relaxed Recursive Transformers: Effective Parameter Sharing with Layer-wise LoRA](https://mlsanity.com/paper/2410.20672/) (2024)
- [LoopFormer: Elastic-Depth Looped Transformers for Latent Reasoning via Shortcut Modulation](https://mlsanity.com/paper/2602.11451/) (2026)
- [Teaching Pretrained Language Models to Think Deeper with Retrofitted Recurrence](https://mlsanity.com/paper/2511.07384/) (2025)
- [Disentangling Memory and Reasoning Ability in Large Language Models](https://mlsanity.com/paper/2411.13504/) (2024)
- [Power Scheduler: A Batch Size and Token Number Agnostic Learning Rate Scheduler](https://mlsanity.com/paper/2408.13359/) (2024)
- [CoTFormer: A Chain-of-Thought Driven Architecture with Budget-Adaptive Computation Cost at Inference](https://mlsanity.com/paper/2310.10845/) (2023)

## Built on by (most cited first, 10 of 10)

- [SMELT: Scaling Laws for Compute-Matched MoE Looped Transformers](https://mlsanity.com/paper/2609.01343/) (2026)
- [Loop the Loopies!](https://mlsanity.com/paper/2607.16051/) (2026)
- [Tying the Loop -- Tied Expert Layers in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2606.16825/) (2026)
- [Allocating Recurrent Compute in Looped Language Models](https://mlsanity.com/paper/2608.18230/) (2026)
- [How to Loop MoE: Flatten the Experts, Untie the Attention](https://mlsanity.com/paper/2609.35751/) (2026)
- [Scheduling Recursive Reasoning in Looped Transformers](https://mlsanity.com/paper/2609.36653/) (2026)
- [Looping Beyond Twice: A Scalable Recipe for Looped Mixture-of-Experts](https://mlsanity.com/paper/2610.01153/) (2026)
- [LoopMoEVR: Loop-Based Degradation-Aware Mixture-of-Experts for Unified UHD Video Restoration](https://mlsanity.com/paper/2610.05109/) (2026)
- [One Model to Loop Them All: Elastic Latent Recurrence for Language Models](https://mlsanity.com/paper/2610.12582/) (2026)
- [LatentLoop: Scaling Looped MoE Models with Asymmetric Compute Allocation](https://mlsanity.com/paper/2610.19975/) (2026)

## Abstract (arXiv)

Mixture-of-Experts (MoE) and looped architectures scale models along two orthogonal axes, namely parameter capacity and effective depth. However, mainstream looped architectures rely on dense backbones that couple parameter count with per-token FLOPs, which makes it impossible to isolate the effect of iterative computation under matched budgets. To this end, we present LoopMoE, a looped MoE language model that integrates sparse routing with iterative weight-shared computation through two designs. The first is IterAdaLN, which resolves weight-sharing symmetry via a modulation signal jointly conditioned on the iteration index and the per-token hidden state. The second is a capacity-balancing strategy that recovers the attention-to-FFN active parameter ratio of well-tuned non-looped references. Together, these designs enable the first strictly controlled, head-to-head evaluation of a looped MoE against a Vanilla MoE under identical total parameters, per-token FLOPs, and active sublayer ratios. Across nine downstream benchmarks, LoopMoE's average improvement over its matched vanilla MoE increases from over 1 point at the 3B scale to approximately 3 points at the 9B scale. These results provide initial evidence that the benefits of iterative sparse computation may strengthen with scale, positioning LoopMoE as a promising architecture for scalable looped language models.