# Closing the Loop: Practical Training Recipes for Looped Language Models

arXiv: https://arxiv.org/abs/2610.00673 · HTML: https://mlsanity.com/paper/2610.00673/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 16 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 14 of 14)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [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)
- [Looped Transformers for Length Generalization](https://mlsanity.com/paper/2409.15647/) (2024)
- [Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers](https://mlsanity.com/paper/2606.18206/) (2026)
- [Think-at-Hard: Dynamic Looped Transformers for Improved Reasoning](https://mlsanity.com/paper/2511.08577/) (2025)
- [HRM-Text: Efficient Pretraining Beyond Scaling](https://mlsanity.com/paper/2605.20613/) (2026)
- [Prioritize the Process, Not Just the Outcome: Rewarding Latent Thought Trajectories Improves Reasoning in Looped Language Models](https://mlsanity.com/paper/2602.10520/) (2026)
- [Loop the Loopies!](https://mlsanity.com/paper/2607.16051/) (2026)

## Built on by (most cited first, 1 of 1)

- [SanSi: A Looped Typed Decision Model for System 1.5 Thinking](https://mlsanity.com/paper/2610.07730/) (2026)

## Abstract (arXiv)

Looped language models increase effective depth by repeatedly applying a shared block of layers, but existing large-scale recipes require multi-stage training over trillions of tokens, while the benefits of recurrence remain difficult to separate from differences in data and training. In this work, we establish practical training recipes for looped language models, with three main results. (1) We develop a compute-efficient from-scratch pipeline that reduces the training budget from 7.7T tokens in Ouro to 310B tokens while retaining strong reasoning performance. Pretraining followed by high-quality mid-training, together with learning-rate warmup and stronger exit-gate regularization, enables stable recurrent training without prior multi-stage schedules. (2) Under controlled comparisons, our 1.4B LoopLM outperforms a parameter-matched dense model trained on the same data and token budget on all 12 evaluated benchmarks, including +14 points on GSM8K, +10 on MATH, and +22 on DROP. At matched inference compute, it approaches a 3.9B dense model on mathematical reasoning and reading comprehension while using only 36% as many parameters. (3) We introduce a minimal recipe for converting pretrained dense models into looped ones: a single learned input-mixing scalar and a smoothed exit loss, with no step-specific parameters. Applied to Qwen3-1.7B-Base, Looped Qwen improves over an identically continued dense baseline on every evaluated benchmark across two data regimes, with statistically clear gains on GSM8K, MATH, and MMLU-Pro on the curated mixture. Together, these results make looped language models substantially cheaper to train from scratch and practical to introduce into existing pretrained checkpoints, while isolating the gains due to recurrence itself.