@inproceedings{yu-etal-2026-spiralformer,
title = "{S}piral{F}ormer: Looped Transformers Can Learn Hierarchical Dependencies via Multi-Resolution Recursion",
author = "Yu, Chengting and
Shu, Xiaobo and
Wang, Yadao and
Zhang, Yizhen and
Wu, Haoyi and
Wu, You and
Long, Rujiao and
Chen, Ziheng and
Xu, Yuchi and
Su, Wenbo and
Zheng, Bo",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.1602/",
pages = "36429--36451",
ISBN = "979-8-89176-459-0",
abstract = "Recursive (looped) Transformers decouple computational depth from parameter depth by repeatedly applying shared layers, providing an explicit architectural primitive for iterative refinement and latent reasoning. However, early looped Transformers often underperform non-recursive baselines of equal compute. While recent literature has introduced more effective recursion mechanisms to mitigate this gap, existing architectures still operate at a fixed, full-token resolution, neglecting the potential efficiency of computing over compressed latent representations. In this paper, we propose SpiralFormer, a looped Transformer that executes recurrence under a multi-resolution recursion schedule. We provide probing evidence that multi-resolution recursion enables the model to learn hierarchical dependencies by inducing iteration-wise functional specialization across different scales. Empirically, SpiralFormer achieves better parameter and compute efficiency than both looped and non-looped baselines across model scales from 160M to 1.4B, establishing sequence resolution as a potential axis for scaling recursive architectures."
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%0 Conference Proceedings
%T SpiralFormer: Looped Transformers Can Learn Hierarchical Dependencies via Multi-Resolution Recursion
%A Yu, Chengting
%A Shu, Xiaobo
%A Wang, Yadao
%A Zhang, Yizhen
%A Wu, Haoyi
%A Wu, You
%A Long, Rujiao
%A Chen, Ziheng
%A Xu, Yuchi
%A Su, Wenbo
%A Zheng, Bo
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F yu-etal-2026-spiralformer
%X Recursive (looped) Transformers decouple computational depth from parameter depth by repeatedly applying shared layers, providing an explicit architectural primitive for iterative refinement and latent reasoning. However, early looped Transformers often underperform non-recursive baselines of equal compute. While recent literature has introduced more effective recursion mechanisms to mitigate this gap, existing architectures still operate at a fixed, full-token resolution, neglecting the potential efficiency of computing over compressed latent representations. In this paper, we propose SpiralFormer, a looped Transformer that executes recurrence under a multi-resolution recursion schedule. We provide probing evidence that multi-resolution recursion enables the model to learn hierarchical dependencies by inducing iteration-wise functional specialization across different scales. Empirically, SpiralFormer achieves better parameter and compute efficiency than both looped and non-looped baselines across model scales from 160M to 1.4B, establishing sequence resolution as a potential axis for scaling recursive architectures.
%U https://aclanthology.org/2026.emnlp-main.1602/
%P 36429-36451
Markdown (Informal)
[SpiralFormer: Looped Transformers Can Learn Hierarchical Dependencies via Multi-Resolution Recursion](https://aclanthology.org/2026.emnlp-main.1602/) (Yu et al., EMNLP 2026)
ACL
- Chengting Yu, Xiaobo Shu, Yadao Wang, Yizhen Zhang, Haoyi Wu, You Wu, Rujiao Long, Ziheng Chen, Yuchi Xu, Wenbo Su, and Bo Zheng. 2026. SpiralFormer: Looped Transformers Can Learn Hierarchical Dependencies via Multi-Resolution Recursion. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 36429–36451, Budapest, Hungary. Association for Computational Linguistics.