# CHASE: Cache-Hole-Adapted Skip Exit for Looped State-Space Language Models

arXiv: https://arxiv.org/abs/2607.10110 · HTML: https://mlsanity.com/paper/2607.10110/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 18 of its 22 references that are in the map.
- First posted on arXiv 11 Jul 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- State-space sequence models (S4, Mamba) / [Core SSM architectures for language](https://mlsanity.com/ssm/core-ssm-architectures-for-language/)

## Builds on (most cited first, 18 of 18)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [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)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [Physics of Language Models: Part 4.1, Architecture Design and the Magic of Canon Layers](https://mlsanity.com/paper/2512.17351/) (2025)
- [Implicit Language Models are RNNs: Balancing Parallelization and Expressivity](https://mlsanity.com/paper/2502.07827/) (2025)
- [Tiny Recursive Reasoning with Mamba-2 Attention Hybrid](https://mlsanity.com/paper/2602.12078/) (2026)
- [LT2: Linear-Time Looped Transformers](https://mlsanity.com/paper/2605.20670/) (2026)

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

- [Improving Test-Time Scaling with Adaptive Looped Transformers](https://mlsanity.com/paper/2609.35748/) (2026)

## Abstract (arXiv)

Recent work on looped language models suggests that many reasoning problems benefit from greater computational depth rather than from additional independent parameters. Existing studies, however, focus almost exclusively on Transformer backbones, leaving open whether this principle also applies to state-space language models. We investigate Looped Mamba and Looped Hybrid Mamba-Transformer architectures, which repeatedly apply a shared Mamba (or hybrid) block to introduce explicit finite-depth recurrent computation. On two controlled reasoning tasks-Mano (modular-arithmetic manipulation) and p-hop induction-Looped Mamba consistently outperforms parameter-matched non-looped baselines and, in several settings, matches or exceeds non-looped models of equal effective depth. We then extend the study to language model pre-training under matched iso-parameter and iso-FLOPs protocols, which jointly disentangle the effects of parameter sharing and effective depth: looped models remain competitive on downstream benchmarks with substantially fewer distinct parameters, although deeper non-looped models retain an advantage in validation perplexity under strict iso-FLOPs comparisons. Finally, we adapt Ouro's two-stage exit gate to Looped Mamba for threshold-controlled selection among recurrent-step outputs. Executing such exits on a state-space backbone, however, leaves the recurrent state without its deeper updates, and validation perplexity then degrades severely. We therefore introduce a cache-hole adaptation that aligns continued training with skipped-state inference. At the scales studied, the adapted model keeps perplexity close to full computation and matches or exceeds full-compute exit-state selection on downstream benchmarks while executing roughly half of the recurrent steps, which translates into measured inference speedups once the prefill is compute-bound.