# Enabling Dynamic Computation in Looped LMs

arXiv: https://arxiv.org/abs/2610.09013 · HTML: https://mlsanity.com/paper/2610.09013/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in KV cache optimization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Placed in

- Efficient LLM inference and serving / [KV cache optimization](https://mlsanity.com/inference/kv-cache-optimization/)

## Builds on (most cited first, 21 of 21)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Mixture-of-Depths: Dynamically allocating compute in transformer-based language models](https://mlsanity.com/paper/2404.02258/) (2024)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [Teaching Pretrained Language Models to Think Deeper with Retrofitted Recurrence](https://mlsanity.com/paper/2511.07384/) (2025)
- [Less is More: Recursive Reasoning with Tiny Networks](https://mlsanity.com/paper/2510.04871/) (2025)
- [Loop, Think, & Generalize: Implicit Reasoning in Recurrent-Depth Transformers](https://mlsanity.com/paper/2604.07822/) (2026)
- [Think-at-Hard: Dynamic Looped Transformers for Improved Reasoning](https://mlsanity.com/paper/2511.08577/) (2025)
- [LoopUS: Recasting Pretrained LLMs into Looped Latent Refinement Models](https://mlsanity.com/paper/2605.11011/) (2026)
- [Training-Free Looped Transformers](https://mlsanity.com/paper/2605.23872/) (2026)
- [ELT: Elastic Looped Transformers for Visual Generation](https://mlsanity.com/paper/2604.09168/) (2026)
- [Memory-Efficient Looped Transformer: Decoupling Compute from Memory in Looped Language Models](https://mlsanity.com/paper/2605.07721/) (2026)
- [Adaptive Loops and Memory in Transformers: Think Harder or Know More?](https://mlsanity.com/paper/2603.08391/) (2026)
- [Nanbeige4.2-3B: Unlocking Agentic Capabilities in a Compact Model](https://mlsanity.com/paper/2607.22083/) (2026)
- [AdaPonderLM: Gated Pondering Language Models with Token-Wise Adaptive Depth](https://mlsanity.com/paper/2603.01914/) (2026)
- [Loop the Loopies!](https://mlsanity.com/paper/2607.16051/) (2026)

## Abstract (arXiv)

Looped LMs are parameter efficient and promise dynamic computation (saving memory and FLOPs on easy tokens). However, state-of-the-art open Looped LMs trained with this dynamic computation capability (Ouro models) do not realize it in practice as each loop iteration (depth) requires its own level of KV-cache, necessitating all loop computations. Moreover, Ouro's early-exit prior is enforced on each token equally, which results in static lower-depth like processing of all tokens regardless of difficulty. In this work, we propose a simple "best-available" KV caching strategy that works out-of-the-box, creating a new frontier in the performance vs depth space. Our approach enables up to 30% reduction in FLOPs and KV memory while retaining full-depth performance, showing the true flexibility of Looped LMs. Furthermore, training looped LMs with awareness about this KV caching strategy improves performance and efficiency. Finally, we apply a small but effective fix to the early-exit prior enforcement objective that makes tokens exit at truly heterogeneous depths based on effort. Our findings are validated on Ouro models as well as smaller looped LMs pre-trained from scratch.